If its Backfiring its a timing issue, period.
What I mean is its a single cylinder engine aka simple ,no valve train ,no timing chain, or camshaft. It only gets signal from the flywheel indexed key or the coil ,so simple deduction would indicate a problem with either of the 2.
If you bought it off the internet it could have the wrong flywheel or coil on it and the part numbers would indicate that.
If the cylinder is messed with ,as in gasket thickness or port timing changed through grinding it could be off ,but visually that would be apparent.
First make sure all parts are correct for the model then test coil leads for correct ohms and resistance, gap setting and connectors at the plug and coil. A backfire may not be what your experiencing but rather losing your spark intermittent.