Must I do something about a sum of money I found four years ago along with a paper from an analysis center that bears no name, given my remorse for not inquiring about the source of the paper at the time?

You were obligated to publicize this found item for one year in places where its owner was likely to be found, or to delegate a trustworthy person to do so. Since you did not, you must repent to Allah.

Scholars differed regarding a found item after one year has passed without publicizing it: Hanbalis: The obligation to publicize ceases after the first year. Malikis and Shafi'is: It must be publicized even after one year, and the finder is liable for it if it perishes. Hanafis: There is no time limit for publicizing it; rather, the criterion is when the finder predominantly believes its owner will no longer seek it.

The most preponderant opinion: The finder commits a sin if they took it with the intention of possessing it, or not publicizing it, or delayed its publicization. They must repent and publicize it anew unless they predominantly believe its owner will no longer seek it. In that case, they should give it away as charity while being liable for it if its owner requests it later. This aligns with the objective of Sharia in preserving rights.