Hi, based on your rank that is 268, hence most probably your general rank range lie in between 30K-45K and your Gen-EWS rank may be lie under 6K. So I'm suggesting only those colleges which comes under Government/Public below.

Note: -The below list doesn't based on any special branch the list will show those top colleges under your rank range which show minimum or lowest branch into the institute as well.

• Dr. Bhimrao Ambedkar University, Agra
• Feroz Gandhi Institute of Engineering and Technology, Rae Bareli
• Dr. Ram Manohar Lohia Awadh University
• Veer Bahadur Singh Purvanchal University, Jaunpur
• University Institute of Engineering and Technology, Kanpur
• Bundelkhand University, Jhansi
• Lucknow University

Etc.

Moreover you can also take help to predict your own college by yourself through Careers360 UPSEE College Predictor tool(link mentioned below) according to your rank in any category;

Good Luck.