See with a degree in Genetics (with a Masters degree preferably) you have chance to get jobs in sectors like:

• Hospitals
• DNA Forensics Department
• Universities
• Pharmaceutical Industry & Suppliers
• Agricultural Firms
• Research Institutes
• Animal Breeding Industry
• Food and drink companies
• Health and beauty care industry

For research careers you may get a JRF at some of the famous institutes:

• NBRC
• ICMR-IARI
• ICMR-DMRC
• NII
• ICAR-NDRI
• ICMR-NICED
• NABI
• IISER
• NIMHANS
• CIMAP
• Tata Institute for Genetics
• NCCS
• CSIR-IGIB
• PGIMER
• CSIR-CCMB
• NIBMG
• TIFR & Many Many More

Some of the notable job profiles you may get depending on your education background are:

• Clinical molecular geneticist
• Clinical scientist, genomics
• Clinical scientist, immunology
• Genetic counselor
• Pharmacologist
• Plant breeder/geneticist
• Research scientist (life sciences)
• Assistant Professor
• Genetics Laboratory Technician
• Regulatory Process Manager
• Nutritionist
• Scientific Writing

I hope this answer helps. All the very best for your future endeavors!