Dear,
JEE Mains provides you admission to the NITs and  CFTIs..On qualifying JEE ADVANCE you will get admission in the IITs .Since these institutions are funded by the government .You will not have to give any donations in these colleges.I will provide you below the list of all the NITs,CFITs and IITs

NITs:

National Institute of Technology, Agartala, Tripura

National Institute of Technology, Patna, Bihar

Motilal Nehru National Institute of Technology, Allahabad, Uttar pradesh

Maulana Azad National Institute of Technology, Bhopal, Madhya pradesh

National Institute of Technology, Calicut, Kerala

National Institute of Technology, Durgapur, West Bengal

National Institute of Technology, Hamirpur, Himachal Pradesh

Malaviya National Institute of Technology, Jaipur, Rajasthan

Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, Punjab

National Institute of Technology, Jamshedpur, Jharkhand

National Institute of Technology, Kurukshetra, Haryana

Visvesvaraya National Institute of Technology, Nagpur, Maharashtra

National Institute of Technology, Raipur, Chhattisgarh

National Institute of Technology, Rourkela, Odhisha

National Institute of Technology, Silchar, Assam

National Institute of Technology, Srinagar, Jammu & Kashmir

S V National Institute of Technology, Surat, Gujarat

National Institute of Technology Karnataka, Surathkal

National Institute of Technology, Trichy, Tamilnadu

National Institute of Technology, Tadepalligudem, Andhra Pradesh

National Institute of Technology, Warangal, Telangana

National Institute of Technology, Arunachal Pradesh (Yupia)

National Institute of Technology Sikkim

National Institute of Technology, Goa

National Institute of Technology, Meghalaya

National Institute of Technology, Nagaland

National Institute of Technology, Manipur

National Institute of Technology Mizoram
National Institute of Technology Uttarakhand

National Institute of Technology, Delhi

National Institute of Technology, Karaikal, Puducherry

GFITs:
Assam University, Silchar

Birla Institute of Technology, Mesra, Ranchi

Gurukula Kangri Vishwavidyalaya, Haridwar

Indian Institute of Carpet Technology, Bhadohi

Institute of Infrastructure, Technology, Research and Management- Ahmedabad

Institute of Technology, Guru Ghasidas Vishwavidyalaya, Bilaspur

J.K. Institute of Applied Physics & Technology, Allahabad

National Institute of Electronics and Information Technology, Aurangabad

National Institute of Foundry & Forge Technology, Hatia, Ranchi

Sant Longowal Institute of Engineering and Technology

School of Engineering & Technology, Mizoram University, Aizawl

School of Engineering, Tezpur University, Napaam, Tezpur

School of Planning & Architecture, Bhopal

School of Planning & Architecture, New Delhi

School of Planning & Architecture, Vijayawada

Shri Mata Vaishno Devi University, Katra, J & K

Indian Institute of Engineering Science and Technology, Shibpur

HNB Garhwal University Srinagar (Garhwal)

International Institute of Information Technology, Naya Raipur

University of Hyderabad

IITs:

IIT Kharagpur

IIT Bombay

IIT Madras

IIT Kanpur

IIT Delhi

IIT Guwahati

IIT Roorkee

IIT Ropar

IIT Bhubaneswar

IIT Gandhinagar

IIT Hyderabad

IIT Jodhpur

IIT Patna

IIT Indore

IIT Mandi

IIT (BHU) Varanasi

IIT Palakkad

IIT Tirupati

IIT Dhanbad

IIT Bhilai

IIT Goa

IIT Jammu
IIT Dharwad

Other than these you can get admission in the IISERs through your JEE ADVANCE ranks and will not have to pay donations.

IISER Pune
IISER Kolkata
IISER Mohali
IISER Bhopal
IISER Thiruvananthapuram
IISER Tirupati
IISER Berhampur

Hi Preet!! through Jee Mains, you will be able to get National institutes(NITs), IIITs and Government funded institutions(GFTIs). the government institutes are definitely NITs and GFTIs. If you get into the NITs (trichy,durgapur,surathkal etc etc), they are centrally funded institues. These colleges have no chances of donation and the admission is done purely on the basis of merit.