I am curious about my ancestry, and would like to learn more about the spread of Islam to the region, particularly the method of conversion (by force, or a more gradual acceptance?). One side of my family has roots in East Punjab, and the other comes from Shahjahanpur in Uttar Pradesh. I also want to know how the Islam at the time of its spread to India had changed, or evolved, since the time of the prophet, and how that influenced the various schools that exist today. I am looking for a historic rather than theological perspective, and I know very little about the topics, so references would be great.
Although not specifically concerned with the Punjab, this thread has links to several past questions on this topic.
Very difficult question to answer, and of course there is always the factor--particularly with the Punjabi side of your family--that just because they were there recently doesn't mean they were always there. From a purely political standpoint, the Punjab first saw Muslim conquest by Mahmud of Ghazni, although there were earlier Arab attempts. This puts a reasonable early bound of about 1000, although Mahmud himself and his successors were generally uninterested in initiating conversions. For the Uttar Pradeshi side, the earliest sustained Muslim conquest would be by the so-called Delhi Sultanate (actually a series of different Muslim dynasties), so around 1200 or so. But of course, the Delhi dynasties tended to be largely uninterested in mass conversion, so for both sides of your family the Mughal period is a reasonable guess.
That being said, conquest is not the only cause of conversion. Muslim Arab and Persian merchants had been on the west coast of India since the eighth century, and there was certainly also traffic through the northeast not long after. Adding to that, India was a fairly open minded place--there were public debates involving Buddhists, Brahmanic Hindus and Muslims throughout the Medieval period. So of course the general patterns of conquest may not have held true for the individuals of your family.
I can recommed a book "tinderbox" by MJ Akbar. He has mentioned extensively how islam entered India and how it changed after british arrival.