Paying back taxes for state - any affect on federal filings for those years?

I filed non-resident returns and paid back taxes to a non resident state this year (2024) for tax years 2017 - 2021. My question is, do i need to file an amended federal return for any of those tax  years due to the state taxes paid (even though late)?

 

I am also trying to determine if there is any potential financial benefit to me with having paid nearly $35k in back taxes over that four year period (not including penalties/interest) either through amended federal returns or if any of these taxes paid could be a deduction for those years or this year? 

 

Perhaps there isn't a way to claim any of this in prior years or current year - but thought I would ask if there was, and if I should amend or not. Thank you for your time and help.