I am using a MacBook Pro Late 2011 model. which version of xcode should I need to download and how?
I have tried to download xcodes, higher 9 using apple developer website but non of these support on (version 10.13.6) my Mac?
I used to build on 10.13 but have updated to 10.14 and the Xcode is now 11.0. So maybe you need Xcode 10.
Your MacBook Pro 2011 is maxed out at 10.13.6, and the highest version of Xcode that macOS 10.13 supports is Xcode 10.1 (https://en.wikipedia.org/wiki/Xcode#10.x_series).
According to https://developer.apple.com/app-store/submissions/, “Starting April, 2020, all apps submitted to the App Store will need to be built with Xcode 11. Xcode 11 requires macOS Mojave 10.14.3 or later.”
So even if you have some wiggle room right now, it is closing.
But you can upgrade your 2011 Macbook Pro to Catalina (10.15) using the tool at http://dosdude1.com/catalina/. There is a walkthrough video there. Be sure to back up before doing this.
Disclaimer: I have not done this myself on a 2011 - I’m using a 2012 - but it is widely attested on forums. I have used the tool to download offline installers of Catalina and Mojave.