I have a 1970 T-120 that backfires only between 3500 and 4000
RPM. I've changed the gas twice, replaced the battery, put in
new jets and air cleaner. Otherwise the bike runs great.  Any
ideas?

Assuming by "backfire" you mean back through the intake. That would indicate valve adjustment or ignition timing. Possibly a len mixture that you can tune out by moving the metering rod up or installing a larger jet. Exhaust backfires or "popping" are more likely caused by unburned fuel mixing with air(from an exhaust leak) and a hot pipe to ignite in the muffler. Also suspect valve adjustment or ignition timing, but any failure(weak coils rich or lean mixture etc.) that can leave fuel unused can cause it. If you have Amal carbs, the slides can wear in whatever spot they were used at most, causing unstable airflow and therefore misfires. If the problem is only one cylinder it could be anything, if both cylinder the check things in common like power to coils or fuel lines. Does the backfire occur only when loaded or will it happen revving in neutral? I hope this helps some. A little testing is worth the work, parts are getting too expensive for "try-ignosis" Pat