Yes, PATRONYMICS is a Scrabble word!

Letter values in Scrabble US: P 3, A 1, T 1, R 1, O 1, N 1, Y 4, M 3, I 1, C 3, S 1.

Is it a valid word?

PATRONYMICS is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

a family name derived from name of your father or a paternal ancestor (especially with an affix (such as -son in English or O'- in Irish) added to the name of your father or a paternal ancestor)

Not playable in Scrabble US: PATRONYM.