Is there a statute of limitations in Ohio for such an invoice?

You didn't say whether your contract with the welding company was verbal or written.  In Ohio there are two different statutes of limitation for matters like this: Verbal Contracts (6 years) and  Written Contracts (8 years)--one of the reasons that there is a statute of limitations is that people forget or lose records after a time.  Whichever period is applicable would start with the date that the work was performed or the date that the payment was actually due, if either of you could prove that.  The problem with no records is that you can't prove much, unless they hand you the proof, such as the invoice that says when payment was due or the work was performed or you have a really good, reliable memory about when the work was performed such as their work was tied to a specific event or contract that you fulfilled that can prove that date.  Of course if there is lawsuit you will have to prove that and spend money on a lawyer to help you protect yourself. The fact that you made a payment on what is apparently a different agreement shouldn't extend the limitation period, but be careful, making any payment on this invoice could extend their right to make a claim/file a lawsuit even after the original period has expired.  If you want to pay them something to make them go away--sometimes it is less expensive to give them a nominal payment than fight a battle in court, even if you win--be sure that you only do so with a written, signed settlement agreement or you use a Paid-in-Full check using that statute. My recommendation is that if you do anything, you hire a lawer first to at least give you some guidance.  Even talking with (any paying) a lawyer who understands these issues for an hour can be less expensive than doing it yourself as cases like this can be very fact specific and the other side will often have/remember different "facts" than you remember.  That is often what court cases are all about and why they call judges and juries "triers of fact." Here is a Statute of Limitations Chart that may be helpful.