Hello kid,
.
The college will be either public, private or autonomous. Public in means government college and private in means non government college where autonomous means affiliated to some university and has its own rules, exams etc. Public cum private college is no where found. You could have seen wrong information.
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Now as you are talking about IIIT sonipat, it's a private college. You can get the details on its official website or on our carrers360 page.here is the link of the college
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https://www.careers360.com/university/indian-institute-of-information-technology-sonipat

Hello dear,

The defining difference between public and private institutions is how they are funded. Public schools are funded mainly by state governments, while private colleges are supported primarily by their own endowment funds and students' tuition fees.

Hope this helps !!