Hiii

For B.tech genetic engineering you can appear in exams like JEE Mains, SRMJEE, VITEEE, BITSAT, JNUEEE, TANCET,
For B.Sc Genetics there is no such entrance, the admission is directly based on the merit of class 12th exams. Only a few colleges may conduct their own CET like the IPUCET fr indraprasth university.
To study abroad you can go for SAT exam. and then apply directly to the university you wish to apply to and check their criteria for admissions.

Hope this helps.
Thanks!