I had a felony conviction in 2002, will it show uo on a background check?

Depends on the check. Unless you've somehow had it sealed or expunged (very difficult) or if you were under 18 then and over 18 now, this will come up on a criminal background check. But not everyone is authorized to do a full criminal background check. A standard internet check or a private investigator doesn't necessarily have access to state records. But the State police, FBI, or anyone with the authority to have them run the check will find it.