I am using adapalene microsheres + clindamycin phospate gel for treating acne...Does it reduce the black spots....If not what is the treatment for that?

No Rx for dark spots. You can try bleaching them with a hydroquinone-containing solution but don't overdo it. They fade with time. I hope you are able to manage your acne long-term with medication -- it sounds like you're off to a good start. Best wishes.
Acne treatment . Acne is caused by overproduction of oil in the skin called sebum and from a bacteria called propiones acnes. The adapelene controls sebum and Clindamycin is the antibiotic. The dark spots may either be blackheads (sebum in the skin exposed to the environment) or scarring. The former is treatable with adapelene. Scarring is not. Note that improvement w/acne treatment takes 2-3 months.