529 college saving plan only affect state tax return but not federal tax return, correct?

There is no federal tax break for contributions into a 529 plan.

The only tax break on contributions is on the state level. Note that not all states offer a tax break, nor do they all have the same limits.

Yes the money contributed in Calendar Year 2021 will me claimed on your 2021 state tax forms you submit in April 2022.

According to the state of Massachusetts this is how you file an amended return:

Filing a personal income tax amended return

Individuals don't need any special form to file an amended return. You will simply need to submit a revised tax return. For tax years 2016 and after, you’ll find a new “Amended return” oval at the top of the form.

For earlier tax years, you can write “Amended return” at the top of your Form 1 or Form 1-NR/PY.

Your amended return must include all schedules filed with the original return, even if there are no changes to those schedules.

Please don't file Form ABT with your amended return or send a copy of your original return with your amended return.

You may be able to file your amended return electronically using third-party software. If filing on paper, mail your amended returns to the same address used for original returns.