What do you think was written on the piece of paper Archie buried with the skull?

One can only speculate. When Archie buries the sixty-million-year-old rodent skull in the desert, he encloses a crumpled piece of paper with it. Leo asks him what he wrote on the paper, but Archie doesn't tell him. He simply says it was "a word."
It's unlikely that the word in question was "Barney," the name given by Archie to the rodent whose skull he'd kept at home for years and which he's now in the process of burying. Perhaps he wrote the word "Stargirl" instead. After all, Leo and Archie do seem to spend a lot of time talking about this fascinating young lady, and burying her name along with the rodent's skull could be seen as a way of moving on, an admission that their long-standing attempts to figure her out have come to nothing.