Is it available to join table with feature layer depending on two fields?
Short answer, no. The answer hasn't really changed from Joining based on multiple fields.
Multi-field joins are not supported in most ArcGIS geoprocessing tools. For example, Join Field—Data Management toolbox | Documentation uses a "common attribute field", not fields. The best approach would be to create a compound-key field based on your multiple fields. You can try to be creative with Make Query Table—Data Management toolbox | Documentation, but there are lots of limitations and caveats going down that path too.
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