The phrase "slightest suspicion" means having the tiniest feeling or belief that something might be wrong or suspicious, even if there is not enough evidence to prove it. Full definition
This, though, is another area where he has been treated with slight suspicion among activists. (totalpolitics.com)
A majority of the Justices went so far as to proclaim, «The Free Exercise Clause commits government itself to religious tolerance, and upon even slight suspicion that proposals for state intervention stem from animosity to religion... all officials must remember their own high duty to the Constitution.» (firstthings.com)
But often I am asked (yes, boring old me), with slight suspicion and narrowed eyes, «What are you?» (lapechefraiche.com)