(ささい) Annoying petty details. (An application form, procedure, etc.)
かい(こまかい) Similar to 些細. You can understand the difference like this:  the procedure is 些細 because it’s full of 細かい details. However, unlike 些細、細かい can also have a good meaning (fine or detailed textures on a work of art), so be careful.
(しゅうねんぶかい) If you want to use ‘petty’ in the sense of a person who is vindictive or spiteful, use this. But it doesn’t exactly fit the English version:執念深い applies equally to grudges that are legitimate as well as grudges like “You ate my doughnut so I’ll get you back next year as you’re about to get promoted.”   PPP