There are a great number of different English dialects in India, based on regional differences. They’ve been developed after the British colonization of India that started in the early 1600s and lasted all the way until postwar time, in 1947. That’s plenty of time for the English language to evolve and find its own… path, let’s say.
All these dialects have been affected by the Indian spoken in the different regions (Hindi, Punjabi, Bengali, etc.) The more known English dialects are Malayali English, Tamilian English and Punjabi English with some more obscure ones being Butler English, Babu English and Bazaar English.
Other than being based on regions, they are (or were) also based on socio-economic positions. Babu English was developed amongst clerks in pre-partition India and has since developed to no longer be confined to clerks. It was characterised by the extremely polite manner of expression. I’m sure you can guess what Butler English originally derived from. It was the English butlers used to communicate with their masters in the Madras Presidency. Hinglish (Hindi English) features English words blending with Punjabi and Hindi.
The different dialects and accents of Indian English vary greatly, some based mostly on the English language while others feature more words from the different native dialects. The long colonial period India had under England definitely left its marks.
I have worked with Diba on this post (make sure to check out her blog!)