If you don't want goldfish then you can't have any other fish in the tank, as goldfish are the only other coldwater fish you can put in there with it. You can't put any tropical fish in there as they need to live in warm water, like pleco's, cory's, catfish, tetra, danios, swordtails, gourami's, betta, clown loaches, cichilds, sharks, angel fish, rasbora's, barbs etc, all need a heater in their water.
Other types of goldfish could be added to your tank such as comets, shubunkin. Then there are your fancy goldfish such as oranda, black moor, veiltail, fantail, and calico etc.
You might be able to put some neons in there if the temperature is raised slightly. I had a friend who housed neons with goldfish successfully.
Although if you add in any of the other goldfish you can only put one more in because they will get too big for the 35 gallons, and ideally they need to be in a minimum tank of 50 gallons.
Have you though of giving up your gold fish and getting tropical fish? There are lots more varieties. Or you could get another tank and get some tropical fish.