Almost every state has the ITI (Industrial Training Institute) from government. They don't have any educational criteria for such courses. Anyone can take those courses and join the labor force or start their own shop.They have the mobile repairing, laptop and desktop repairing and also few other hardware repairing courses. Most of these courses are often run based on the expert faculty available for that semester.
Do also note that each state or city may have it's own ITI center. So you may find city or state specific website. In case of Mumbai they have the following address and website.
Address: Industrial Training Institute Mumbai
374, Sane Guruji Marg, Near Agripada Police Station, Mumbai, Maharashtra 400011
Apart from government institutes you have an option to join private institutes such as the following : -
1. Mobile Repairing Course IMET, Lalkurti, India
2. Britco & Britco Mobile Repairing Training Institute
3. Hitech Mobile Repairing Institute, Delhi NCR
4. Max Mobile Training, Hyderabad
5. Jetking Hardware Institute (Pune, Bangalore, Mumbai, Chennai, Delhi NCR)
I suggest finding jetking nearby your city. As they are quite popular for such training, you may find their training option much better compared to many new institutes which are yet to establish.