The original phrase in English was Just what will we come across this time?, but I doubt there is such a word in Latin that expresses humility in this sense, so I just threw just away and came up with Quendam modo inveniemus?, but I’m still not entirely sure about the pronoun and its case, the tense (present or future), and the sentence itself. Any thoughts?
It is not necessary to throw the "just" away; the exasperation expressed by it (if that is indeed what you want to express by it---you speak of "humility," which I do not quite understand) can be approximated with tandem.
Quendam means "a certain person" and is not an interrogative, so it is out of place here. Latin for "what" is simply: quid?
Finally, "this time" is arguably the most difficult part. Modo does not seem appropriate; one could say nunc, but that does not express the idea of repetition (i.e., that this is not the first time we come across something) as the English does. I would prefer the ridiculously literal hoc tempore, although it, too, really only means "now." But at least it implies that there may be or have been alia tempora.
So we end up with:
Quid tandem hoc tempore inveniemus?