Can i contribute to a roth ira after filing? Is there paperwork involved?

Yes and yes, as long as you do it by the filing date. While nothing will change dollar-wise on the return, you will need Form 8606 to keep track of your contribution. You will need to amend.

While the IRS says, "You don't have to file Form 8606 solely to report regular contributions to Roth IRAs. But see What Records Must I Keep, later. File 2021 Form 8606 with your 2021 Form 1040, 1040-SR, or 1040-NR by the due date, including extensions, of your return", they also say:

What Records Must I Keep? To verify the nontaxable part of distributions from your IRAs, including Roth IRAs, keep a copy of the following forms and records until all distributions are made.

• Page 1 of Forms 1040 or 1040-SR (or Forms 1040A, 1040-NR, or 1040-T) filed for each year you made a nondeductible contribution to a traditional IRA.

• Forms 8606 and any supporting statements, attachments, and worksheets for all applicable years.

• Forms 5498, IRA Contribution Information, or similar statements you received each year showing contributions you made to a traditional IRA or Roth IRA.

• Forms 5498 or similar statements you received showing the value of your traditional IRAs for each year you received a distribution.

• Forms 1099-R or W-2P you received for each year you received a distribution

Form 8606 instructions