May I ask 2 questions.
1. Years ago, (being self employed) I had some income tax problems and did not file for years. I finally filed and paid my back taxes on an offer and comprise. I just turned 62 and filed for my SS but 4 of my top years were not credited. At the SS office they said it was due to the fact that I did not pay those years within a 3 year 3 month 14 day time period(?). Is this correct? If so is there any way around it?
2. My wife worked for 5 years paying into SS and then worked 28 years for City government paying into a pension system in place of SS. She is now collecting her pension and currently does not have enough credits to collect SS. Can she piggyback on my SS.
If you didn't file tax returns and pay the appropriate self-employment taxes on your earnings within 3 years, 3 months and 15 days following the years in question, you can't receive Social Security credit for your earnings in those years even if you subsequently paid the correct taxes. This is referred to as the 'Statute of Limitations', and it doesn't sound like you would meet any of the exceptions to the regulation(https://secure.ssa.gov/poms.nsf/lnx/0302201008#a1).
Although your wife would likely technically qualify for spousal benefits on your record, her city pension would preclude her from receiving benefits if it amounts to more than 2/3rds of the amount of her potential spousal benefit. This is due to the Government Pension Offset (GPO) provision: https://www.ssa.gov/pubs/EN-05-10007.pdf. She could still qualify for Medicare on your record at age 65, though.