If you can join your adjacent flat with your flat as one flat, it may be considered as one single dwelling unit. It is then a self occupied house. There is no rental income on such property.
If you cannot join your adjacent flat but it is still very nearby, it can be still considered as one single dwelling unit, but such presumption is not free from disputes and you may have to prove it so at appeal levels.
If you have taken a housing loan, you may claim interest on housing loan on such self occupied property upto Rs. 2 Lakhs. This is in respect of existing loan, if any, and the new loan you may take. However, if the interest component exceeds Rs. 2 L, it may be worthwhile for you to let out the new house to your parents and claim interest actuals without any limit. You will have to evaluate both the options and decide.