A lot of authors pay to be published... but you don't find their books in bookshops. If you don't believe me, go to your nearest large bookshop and see if you can find anything published by this company. Ask the staff if they've even heard of the publisher. I'll bet they haven't.
If a publisher says they will share the cost of publication with you, they're almost certainly lying. You'll pay all of it.
Maybe things are different in India, but where I live, if you pay to have your book published, you'll have to do all the marketing yourself. Bookshops won't stock your book, because they know that companies like Leadstart will print anything, so almost all the books they print are bad. (Leadstart make their profit when you pay them to print your book, so they're not going to do anything for you after that, because that would just reduce their profit.)
The way it's supposed to work is that the publisher selects only the best books to print, and pays for everything - editing, cover design, marketing, distribution. They usually pay you some money upfront (this is known as an advance) and then some money for each copy that they sell.
The way that Leadstart and companies like them work is that they print every book they receive, and the author pays for everything. Because they're guaranteed a profit on everything they print, it's not in their interest to reject any book.
If you haven't signed a contract yet, don't. If you have signed a contract, get out of it as soon as you can. Don't give them any money if you can possibly avoid it, and spend some time learning how the process is supposed to work.