I am planning on making a service that uses a modified open source software. Would it be legal for me to profit from it? I am not sure what information would be relevant to this so if I have missed some relevant info, please tell me what additional information is required to determine this.
Yes, you can use open source software commercially. The Open Source Initiative (OSI) says:
Can Open Source software be used for commercial purposes?
However, note that commercial is not the same as proprietary. If you receive software under an Open Source license, you can always use that software for commercial purposes, but that doesn't always mean you can place further restrictions on people who receive the software from you. In particular, copyleft-style Open Source licenses require that, in at least some cases, when you distribute the software, you must do so under the same license you received it under.
When using code from a copyleft license, the question then becomes whether you need to share your derivative source code. This depends on which copyleft license was used and what your program is doing with the code, as some licenses have what is known as the SaaS loophole which would allow you to use copyleft code server side without needing to release your code.
See also OSI’s list of open source licenses.