How we can develope for ArcGIS Extension for ArcMap or ArcGIS Map Services ?

VBA/VB was the best solution to customize the ArcGIS and extensions since ESRI has dropped the VB environment and most rely on Python, which is integrated in ArcGIS package itself, you can also use other coding languages too to develope ArcGIS and its extensions.

ArcGIS supports Java

But most of my colleagues use Python, a lot

And I would suggest to start there

Python is a programming language that resides inside ArcGIS, ArcMap and other related

But if you are referring to App extensions, then it is in java (with or without Python)

Hope this helped