How can I use my ArcGIS for server maps instead arcgis.com maps
I'm assuming you're referring to using an ArcGIS Server map service in the ArcGIS Online map viewer for your web map instead of the basemaps provided there.
If this a map service you are hosting on your own server, see the following steps:
1. Click Add, and choose Add Layer from Web
2. In the first drop down, ensure An ArcGIS Server Web Service is chosen. In the URL section, enter the rest endpoint for your map service.
3. Ensure you check the box beside "Use as Basemap"
You can also refer Choose basemap—ArcGIS Online Help | ArcGIS for more information, and instructions on how to change the basemap from searchable layers on ArcGIS Online.
Thank you very much for your answer.
Jennifer's advice is spot on if you were not aware of that already. The other option is to use the Local Layer widget LocalLayerWidget Version 2.5 and AccessifizrWidget Layer - 09/28/2017 this allows you to add layers from your own ArcGIS Server right into WAB from the WAB UI. There is still an unfortunate need to initially have a webmap as a begining point and then the Local Layer widget can completely replace the contents of the initial webmap or just add to it.
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