Which preposition to use with cavillings

of Occurrences 2%

His teaching, in spite of the vehement cavillings of the "antis" of his day, gained credence readily, and vaccination speedily became recognized and was constantly resorted to, but hardly any attempt at perfecting the practice was made until after more than fifty years had elapsed.

by Occurrences 1%

" The Chamberlain family, however, being more or less smart, spry men, were doubtless sharp enough to detect some inkling of this sort of feeling, and consequently they thought it better to silence any such cavillings by eschewing as far as they could public life, and contenting themselves with being brothers of a big man and sharing a little reflected glory.

on Occurrences 1%

It is difficult to say of which there is most in the world, a blind belief in religious dogmas, or a presumptuous and ignorant cavilling on revelation.

Which preposition to use with  cavillings