JSON Schema is not intended to be feature equivalent with XML Schema. There are features in one but not in the other.
In general you can create a mapping from XML to JSON and back again, but that is not the case for XML schema and JSON schema.
That said, if you have mapped a XML file to JSON, it is quite possible to craft an JSON Schema that validates that JSON in nearly the same way that the XSD validates the XML. But it isn't a direct mapping. And it is not possible to guarantee that it will validate the JSON exactly the same as the XSD validates the XML.
For this reason, and unless the two specs are made to be 100% feature compatible, migrating a validation system from XML/XSD to JSON/JSON Schema will require human intervention.