I think I can help you out with that, the answer to 'pesky little twerp' in the NY Times crossword is probably 'imp', it's a common term used to describe a mischievous or annoying child, and it's a word that often shows up in crosswords, but if that doesn't fit you can also try 'brat' or ' pest', see if either of those work for you, let me know if you need more help or if you have any other letters that might give a clue.
