Jamming by being pulled in on one side but not the other, could be owing to paper path blockage... be sure to peer deep into the printer in that region to make sure other debris or paper is not clogging or blocking the paper path on the side that doesn't feed in... or it could be owing to one roller, the one that doesn't feed, needing cleaning:
If the problem might possibly be owing to aging roller surfaces (for paper is fed into faxes and printers with rubber or plastic cylindrical rollers, that propel the sheet into or through the machine)... then you might need to clean the rollers in the problem area where feeding is not happening.
Remove all paper from the machine, unplug it, and open it so as to have access to the rollers in the problem area where feeding is not being done properly.
Take a clean high-quality lint-freerag cloth, moisten it with rubbing alcohol, and rub the rollers firmly all over their paper-contacting surfaces, three times over.
(If the rollers are hard to reach, there is another way to clean them... let me know if that is the case, and I will detail how to do the cleaning.)
Allow 5+ minutes for drying-off, then reload the paper, close up the machine where you opened it up, and then try again.
Let me know what you think, what you find out, and what happens, please. Thanks.