MSW

https://www.masterstudies.com/Masters-Degree/Social-Work/France/
Hopefully, this link will help you.

Hi,
MA in social work is a 2-year post-graduate degree which aims to equip a candidate with the knowledge of social practices and prepares them to work for the welfare of the society. The minimum eligibility for admission to MA social work in India is a Bachelor's degree in any stream. Admission to MA in social work in India in most of the institutes is done through an entrance test which is generally conducted in the month of June or July. However, there may be an additional round of personal interview which may be conducted by some universities.

I don't think so that the college will allow you to take admission in the final year. However, I would suggest you contact the college officials for more clarity.
Admission is possible only if you get a NOC from your current university.

As MSW is a Master's degree program, any graduate can pursue it. However, it is important that you check your interest after MSW.

Hello Shivani,
I think Banasthali admits students without any aptitude test. One only needs to have requisite eligibility for the course. Staying in the hostel though is compulsory. I am attaching a link that will give you all the required information about this university. http://www.banasthali.org/banasthali/admissions/index.html.