What is this small black spider found in NY?
It resembles a juvenile Phidippus audax, of the family Salticidae.



Image Source: SpiderZule

According to Wikipedia >>


  They are typically black with a pattern of spots and stripes on their
  abdomen and legs. Often these spots are orange-tinted in juveniles,
  turning white as the spider matures.


Phidippus audax is a common jumping spider in North America and definitely not an invasive species.