Can you help me to file an amended state tax return for 2021?

See this TurboTax support FAQ for amending a state tax return - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/need-amend-state-return/L3hGFyaPp_US_en_US?uid=lcl2i94q

Not sure what you mean when you say TT "let" you file without entering your Social Security.  How would the software know that you received SS if you did not enter it?  You were supposed to enter your SSA1099's on the federal return.  Information flows to your state return from the federal return.  Are you in one of the states that taxes Social Security?  If not, you do not need to amend your state return.

States that tax Social Security benefits:

CO, CT, KS, MN, MO, MT, NB, NM, ND, RI, UT, VT, WV

These states offer varying degrees of income exemptions, but four mirror the federal tax schedule: MN, ND,VT, and WV

To Amend a State Return:  https://ttlc.intuit.com/questions/2824532-i-need-to-amend-my-state-return