Headlines for 2021 February 22 read "Supreme Court Approves Subpoena for Trump's Financial Records".
Since the Supreme Court has now ruled on the matter, I am not aware of any other body to which Donald Trump can legally appeal.
What happens to Donald Trump if he refuses to turn over all the financial records for which he has received a subpoena?
According to this Washington Post story:
Vance is seeking the records from Trump’s longtime accounting firm, Mazars.
Thus Trump himself will not be able to refuse to provide the tax return information. Should the accounting firm refuse, it could be held to be in contempt of court, and fined. It is even possible that a responsible person from the firm would be jailed until the firm complies.
I do not see what additional appeals or legal recourse there might be against turning over the returns. But I cannot say that none could be available. There might be arguments that lawyers for Trump or the accounting firm could still raise.
News stories published on 23 Feb 2021 say that Mazars intends to comply with the subpoena. The New York Times story "Supreme Court Denies Trump’s Final Bid to Block Release of Tax Returns" said:
The firm has said it will comply with the final ruling of the courts, meaning that the grand jury should receive the documents in short order. On Monday, Mazars issued a statement saying it “remains committed to fulfilling all of our professional and legal obligations.”
The recent SCOTUS ruling on the ability of the Manhattan DA's office to enforce their subpoena applies to the accounting firm Mazars (who has copies of the tax returns and acts as Trump's agent in dealing with the IRS) and not Trump himself.
"...Vance is seeking the records from Trump’s longtime accounting firm, Mazars." Supreme Court rejects Trump's final bid to shield tax returns from Manhattan prosecutor - The Washington Post
If Mazars does not comply, it and individuals (staff or board or corporate members) can be held in contempt and jailed and/or fined.
There's little reason for Mazars to fight the subpoena; their reputation and livelihood would be at risk if they violated the law and ignored the subpoena. Trump is simply a Mazars client, and they act as his agent.
Vance... had subpoenaed the records from the Mazars accounting firm... Mazars has said it would comply with the subpoena, but Trump (had) sued to block the records’ release. Supreme Court won’t halt turnover of Trump’s tax records - The Washington Post
And, it's important to note that
"The court’s action does not mean Trump’s tax records are to become public. Vance has said they would be protected by grand jury secrecy rules..." Supreme Court ends Trump's bid to shield his tax returns, efforts to challenge election losses - The Washington Post
Update: and note that probably due to that ruling, on March 2nd,
A U.S. House of Representatives panel reissued a subpoena seeking Donald Trump’s tax and financial records, saying in a memo made public... it needs the documents to address “conflicts of interest” by future presidents. U.S. House panel reissues subpoena for Trump's tax records | Reuters
Well, if one defies a valid subpoena, then one is in contempt of court. It's a state court subpoena that they were wrangling over, and I think generally contempt of court is a misdemeanor in the state system. Don't ever try to defy a valid subpoena!
Donald J. Trump may not appeal to any other U.S court because the Supreme Court approved the subpoena. The United States supreme court is the highest court in the nation. So any judgment made by SCOTUS is definitive and no other court can rival.
The IRS can punish him and force him to do it as an act of law enforcement Since the supreme court is the highest court in the land the IRS would recognize Trump will appeal no more.
