Want to be able to solve any software or os related problems of any mobile.

You will need to learn smartphone repairing course from a reputed institute. You have not specified whether you want to set up a repair shop as in the case of hardware repairs. It would be a wiser idea to hire a qualified technician who has the skills rather than attempting to do it yourself. Maybe, you can learn from him so that you will gain expertise in carrying out some minor repairs yourself.

There are a few institutes which provide training in the field. Look for a institute that offers such courses in your neighbourhood. Whether the institute is accredited or not should not be a big deal as you want to set up a shop yourself.

There are some online courses available that claim to teach cell phone repairs. Checking them out could be a good idea.

Prizm Institute is one such firm involved in conducting online courses. If you are above 12 years of age, you can join the course. Only prerequisite is the basic knowledge of computers. Educational qualifications or experience are immaterial. The course uses DVD for practicals and handbooks for the theory. There will not be any online tutorials. Technical support is provided for a period of one year.

Here are the contact details -
Address-
7, Building No 84, Near Station, Nehru Nagar, Kurla East, Mumbai, Maharashtra India. 400024

Phone: +91 22 2523 1122

Mobile: +91 9773 196 196 / +91 9221 288 068

Email: info@prizminstitute.com

Before proceeding, kindly check for the credentials of the institute.

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

Website: http://www.dvet.gov.in

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.