My kids love homemade chicken fingers and its easy and super cheap. I just buy boneless skinless chicken, brush it with olive oil, then bread it in italian bread crumbs with some parm cheese and pepper, a little paprika and basil.
I either make them in strips or in little chunks like popcorn chicken and then bake them. And then I make a cheese mustard sauce to dip or they use plumb sauce.
Crackers and hummus, my lo loves hummus, the pepper garden one.
Make mini sandwiches, like ham and cheese and pb and jam, if no allergies etc....
Mini meatballs would be good too.
Its not a finger food but a cold pasta salad would work too, most kids love anything pasta. lol
Oh maybe a ry bread and some spinach dip, my kids are crazy for that stuff.