Intrusion by neighbour living in below flat

Hello Respected Sir/Ma'am, I am 26 years old. And the resident of an apartment since 22 years, living with my family consisting of my parents & one younger sister. My neighbour living below our flat always picks fight with us regarding our terrace amd claims it to be his own property. My father purchased the flat in which we are living. But he says that the terrace which we use, is his property actually! (He never shows any document for that though). Whenever we try to do any work like, placing the cooler or drilling work or even decorating plants pots; he creates the fuss that we're going to break his terrace. And he always puts false blames on us that because of our work on terrace, his ceilings leak, which is a complete lie!!! He also sends his workers to climb the fence of our terrace to clean it every Sunday without our permission, and whenever we deny it- he claims our terrace as his property and threatens to call the police. Today, he indirectly threatened to shoot me by telling a story of a man, who shot another man for spreading trash on his property. My family has always tried to NOT cause any problem to him. Every year we coat our terrace with cement to avoid any cracks which could cause any possible leakage in his ceiling. We even called our plumber to fix and elongate the pipe connections so that all the water may flow directly into the ground. We even keep our terrace clean so that he doesnt complains. But he keeps on sending his men in our terrace without our permission, violating all the privacy. My new expensive shoes also got stolen from my terrace. And now he has also started to speak bad about my father & me. I want to know what legal actions can I take against him. Please help! This has been going on for many years. But now, its getting out of control. Thankyou??