Can I give IIT JAM Physics for MSc in it while being enrolled at BSc Computer Science?

B.Sc, computer science people are not eligible to get admitted into M Sc, Physics, So after completing B.Sc computer Science trying for MSc Physics is not the correct answer for your problem.
My suggestion is that you should convince your parents that you are not able to cope up with the subject of computer science as you have no interest in that subject and you can not complete the course within the defined period and after that getting a job will be difficult and you should say that you will go for B.Sc Physics only. Even though you are losing one year, I suggest you try this route and join in B.Sc Physics. If you can't convince your parents you have to get adjusted to the time and see that you will get the degree and scope for computer Science is good for getting a job.

If you are interested in doing your studies in Physics then you have to convince your parents that because it is your interest area you can excel in that and going for B.Sc. computer science will be a futile exercise as due to lower level of interest in that you will be a loser. If they are not convinced take the help of a teacher or lecturer who can help you to convince your parents. Please note that a person can do good work in the area he is interested and it is always preferred to pursue a line of liking rather than something thrust upon oneself. It is a question of your career and you should not compromise with your parents in this matter. I think you can convince them by showing them the future prospects in Physics line versus computer science career. Spell your things in precise and clear manner to them and put your points forcefully and with conviction. Tell them that it is not a fascination but a real interest in Physics.

Anyway, if you do B.Sc. computer science then you will not eligible for M.Sc. Physics through IIT JAM route as the eligibility criterion will not be met and you will not be able to apply in IIT JAM.

You have two options at present either convince your parents or go for computer science. Do not think that computer science is a dull area. Today it has emerged as a big discipline and it has overlap with physics when it comes to connecting softwares to scientific machines and equipments where most of the things are governed with the principles of Physics. We are entering the age of automation and robotics where all the sciences are getting merged and Physics is also one of them. So do not have a notion that if you are going for computer science then you are leaving Physics behind. In advanced stages all the basic sciences merge with each other. We are having integrated technologies today. So do not be hopeless and fearful and go ahead and take the challenges of learning computer sciences.

I think I will cite one example here that one of my friend who did with M.Sc. Physics joined petroleum industry. He told me that there are many subjects like Geology, Chemistry, Reservoir engineering etc which are required by him in his job and Physics was to kept at the background only. To get success in his career he had to learn many things related to above subjects and then he came to know that there was a lot of merging of disciplines at the working level. His basic degree was only a via media to get that job. I hope you get my point and understand the context.

If you are not comfortable with B.Sc in Computer - science, it would be nothing but sheer time loss. I would say you must have guts to convince your parents of the final outcome on being persued this subject.
Now to achieve your objective, there are twin ways to achieve the same. You may write JEE examination but before that you have to ensure your marks of class 10+2, the combined aggregate marks for Physics, Chemistry and Matyematics should not fall less than 75 percent. This is the essential criteria to be fulfilled. Then the second stage is to qualify both JEE main and JEE Advanced with some respectable ranking making you eligible to be inducted in the 5 year programme for Physics. IIT being a premiur institution and having passed out with Physics from this Institute would provide you immense scope for the doctorate degree in Physics, joining some govt Research Institute, Atomic Energy Commission Trombai etc.
The other means would be to opt for a reputed college in the next session for Physics ( Honours) provided you satisfy the eligibility criteria of such college. They would consider your Physics marks of your 10+2 stage. In case, you manage to qualify the eligibility criteria, you can pass out B.Sc ( Honours) with grand marks provided you exert right effort. With the impressive marks in the graduation stage, admission in M.Sc ( Physics) can be secured in some well established university.