Are the laws that apply to a public property apply to a lane?

I don't have any knowledge about the areas of law. I don't know that the jurisdiction over a lane come under Constitutional Law but I have done it here so I get some answers.So if I am wrong please bear with me.My set of questions are as follows: 1.Is a lane(here in India-mumbai we call it a "gully") having same legal bindings as any public place ? 2. Please refer me to some books and sources to get more information about the topic? The reason I ask this is because I have a neighbour family which is very noisy especially around our entrance area in the lane and they treat the entire lane as their own private property and if we say to not treat it as a private property they say it's public and who are you to tell us what to do in the lane . Since we have said them many times they have turned a verbally abusive attitude towards us and sometimes they have turned violent against us (in the past they have and we have booked a non-cognizable complaint against them in police station) Now as they have shown their violent sides I have chosen not to be afraid of them and restore everything right through the law. Note: We have never done any harm to them in any way and would further be working only through the law by not taking law in our own hands. Thank you for reading. :)