I found an odd sized cent last night. It looks just about like the regular 1913 cent but when I tried to put it in a new coin book hole it just falls right back out without any problem. All the rest of the cents I tried in the hole bairley fit. The lettering also seems closer to the rim. I would post a picture but I am not at home at the moment.
Different hole Different hole filler problem. Have you placed it in a stack of cents? I'm guess the small one is what you are talking about.
You could use a Cyanoacrylate adhesive to bond the coin into the hole. If there is a big gap, then you could use 2-part epoxy to fill it. However, this may irreparably damage the coin & coin folder. The weight of the coin & the detailed characteristics of the edge would be nice to know.
I think the key is the part of the description about the lettering being closer to the rim. Classic description of a dryer coin. Especially one that has only been in the dryer fin long enough to have the diameter reduced slightly but not so long as to make the broadening of the edge overtly noticable.