I want to use osm map and I want to have offline routing in my android application .
what should I do ? can you help me?
For the OSM tiles offline, you'd need to obtain the tiles yourself somehow and then implement your own tile handler, in much the same way that this sample here does it: Local MBTiles | ArcGIS for Developers
For the offline routing, you can take your network dataset and side-load it to your device and use the RouteTask API to find routes, as described in this section of the guide: Finding a Route—ArcGIS Runtime SDK for Android | ArcGIS for Developers
I hope this is helpful to you.