Is this a famous song that you did not write or sing originally, but you did perform your own vocals or play your own instrumentals of the song?
Transformative works, such as covers, fall under fair use. Consider that Elvis' two most famous songs, "Blue Suede Shoes" and "Hound Dog" were not originally written or performed by him, but other people. Elvis just did the cover better. Parody artist Weird Al Yankovich does ask original performers of his parody songs if they are okay with the Parody before releasing them, but this is out of politeness, not legal burdens (most artists see it as a sign they made it big in the music business if he asks them and gladly agree. Of the rare few who refuse, Michael Jackson was a noted fan who had been mocked once already but didn't want the particular song "Black and White" to be parodied because he didn't want the message about racial tolerance to be lost in the parody. He instead offered other songs and the complete sets to his music videos for Al to further parody. Lady Gaga found out her agent said no without consulting her and reversed the decision because she was such a fan. Al now goes out of his way to ask the artist directly, rather than through third parties like the record company (in Coolio's famous feud with Al) or agents.
In the end run, the decision to sue some one over song (or any entertainment media) copyrights boils down to how much damage you are causing to the initial product (how much money your derivative work makes over the original work or proof that your work adversely affects the original's reputation or sales). In DC vs. Fawcett comics, DC sued Fawcett because their character Captain Marvel (now called Shazam, cause no relation to Marvel Comic's Captain Mavel) closely resembled Superman and some art was done that came close to famous Superman art. At the time of the suit, Superman knock off comics were a dime a dozen and the earliest came out pretty quickly in Comic Book production terms to the first Superman story. However, Fawcett had managed the one thing Superman had not, which was it was actually beating Superman in sales, which is why it was targeted (irony was, Captain Marvel flew before Superman). So, your threat of suit is really likely if the owners of the song's rights are threatened by your performance.
The fact that it is not copyright infringement means nothing to can you be sued. You can be sued for looking at someone the wrong way (the court will likely throw it out.). Most music companies are based in California which has tough Anti-SLAPP laws designed to prevent big media from silencing people by suing them for legit protected speech. By filing charges to drop the SLAPP, the judge will have to look at the merit of the cease and desist and can stop the whole litigation process right then and there on the grounds the plantif is just suing you to shut you up. If that doesn't work, prepare for a long haul as these cases are notorious for dragging out.
Additionally, in the United States, Fair Use is a quasi-affirmative defense. Until recently, the defendant must assert it as a defense in a particular case and the burden of proof that it was Fair Use is on the defendant (i.e. if sued and you do not claim Fair Use even if it is, the judgement will likely not consider it and find in copyright infringement). This has been changed with relationship to DMCA copyright infringement take downs so that, if you're releasing on the Internet, the copyright holder must take fair use into consideration before issuing a take down notice (i.e. If you post a video to Youtube and the copyright holder wants to take it down, the copyright holder must make sure there is not a chance you will use Fair Use as a defense if a suit is brought up.)
Fair use has four weighted components. No one component is a hard weight against you or in favor of you as with all free speech matters, context is king. First, is the nature of the use (for what purposes are you using the work and how did you use it). Second is the nature of the work (what breech of the work itself constitutes fair use. Historically significant items, like the Zaputer Film of Kennedy's assassination, may override the copyright. Quality of the work does not factor in here.). Third is the nature of the amount copyrighted (This is not a hard number, as 400 words out of 20,000 can be considered infringement if those 400 words would impact purchase of the original text. Conversely, a VCR (DVR before DVRs for you youngin's) recording of a television show in it's entirety is not infringing as you are merely choosing to enjoy the work at a later time and not reselling it.). Finally, damage to the original product (Money, dear boy. Again, recording full TV shows is fine if you are intending those recordings for personal use).
While not official factors, attribution might be taken into consideration. It's important to remember plagiarism and copyright are not the same thing. If you were to sing a Justin Beiber song without saying it is a Justin Bieber song, that is plagiarism but still Fair Use (by adding your own voice, you are making a transformative work), even if you claim the ideas as your own. You would be a terrible person, but in the eyes of the law you did nothing wrong. However, if you post Justin Beiber's original song to the internet for download purposes, and cite it as a Justin Bieber, this is copyright infringement as you have not been authorized to distribute Bieber's music for a lower (or in this case no) price. At this point, it's too late to say sorry.
Finally, and please be cautious about this, but the model as I understand it is that you are posting your rendition of the song (you sing it, not the original performer) to a Patreon like site. If people are giving money to you and not necessarily buying your song (you aren't charging a download fee, you're charging for appreciation of your talents?). You can incentivize donations by access to additional perks such as early releases or access to additional releases. So long as you are not being paid for a song itself, but the enjoyment of your songs, it will be hard for the Beeb's lawyers to ague you're making money off of his song and not, say, your rendition of Frank Sinatra's song. The same work's in reverse because Sinatra's lawyers need to prove you aren't getting paid for The Beeb's work. As long as you maintain your customer base is paying for your songs because of what you bring to them with your own musical talents, both Beebs and Frankie are losers and you don't even have to bless them all. The more transformative this can be (including different arrangements of the music, such as singing Beiber songs in the style of Sinatra and Sinatra songs in the style of Beiber, or different arraignments or lyrics) the better. The more of your own work you put into it, the better. If you want to be educational about it (did you know you can sing the Original Pokemon Theme, the Original Teenage Mutant Ninja Turtles theme, and the Ballad of Gilligan's Island to the tune of each other?) that's good. Remember, the idea of "Baby, Baby, Oh" is not copyrighted and cannot be. Justin Bieber's way of expressing that idea is.
Two final notes. In the United States, the royalties of the song go to the author and the record company that sells it, which need not be the artist who sings it. They are paid because people want to hear them sing it (Frank Sinatra and Elvis both are famous for songs that they did not originally sing. People would pay for them specifically to sing it and the authors and record companies didn't care, because they were getting paid because someone was singing it.). In this case, it pays in the states to know which songs are sung by their authors and which sung by not their authors. This is unique to them.
Also, all Fair Use stuff is United States in case law. It is a common law statute meaning it will be considered by most countries that were once apart of the British Empire or a part of something that was apart of the British Empire or that the United States or Britain had significant hands in building (Over 2 billion served!), but the United States has some quirks with regards to Free Speech (namely, all speech is considered Free Speech until proven otherwise) so check your local Fair Use equivalent if not in the United States (though being a big media exporter, U.S. copyright law is influential the world over).