Seldomly is an unnecessary variant of seldom. Seldom is already an adverb, so adding the adverbial -ly doesn’t change its meaning. Using seldomly is not a serious error, however. Your spell check probably catches it, and most major dictionaries either don’t list the word or list it as obsolete, yet to many English speakers, seldom without the -ly just doesn’t feel right in certain situations (a similar effect is seen with thusly, an unnecessary variant of the adverb thus). If you are an English speaker and you think seldomly sounds better than seldom in a sentence you’re writing, there is no reason to go against your instincts.
This is not a case where the adverbial suffix has been dropped from a word that once ended in -ly. Seldom goes back to Old English (and through the centuries it was variously spelled seldun, seldenn, seldon, seildunn, and seeldum, until the modern spelling was settled around the 18th century), and it has always been an adverb. Seldomly first appeared many centuries after seldom had already been in use, and it was never the standard form. Still, in this case even the superfluous form is many centuries old.
Deblinger says children seldomly come forward to report their abuse . [ABC Local]
When talking Michigan football, the word “inexperienced” is seldomly used. [Collegiate Times]
The characters look so poorly aliased and their dialogue matches their mouths so seldomly that the game looks like it was created by a ’80s-era Japanese studio. [Auburn Pub]
[T]he laptop remained mostly quiet and the fan was only heard seldomly. [PC World]
You should also make sure that your children seldomly eat outside the home as this can help reduce contaminated food intake. [Sunday Observer]