I am using Databricks provided ODBC driver to connect JMP 18 to Databricks. When I try to connect the connection is successful, but I am not getting the list of tables/ catalog/ schema to bring the data in JMP.

I tried to refresh multiple times, but it does not work
This sounds a lot like:
https://community.jmp.com/t5/Discussions/JMP-ODBC-Databricks-and-default-catalog/m-p/670654
The gist is:
This is most likely due to the connection string missing:
Catalog=
where is the catalog where your data is. There are many drivers that do not persist , so JMP doesn't know there is one.
For instance, in say, Open Database, you'd modify it like (adding the Catalog=entry):
Open Database(
"Driver=Simba Spark ODBC Driver;Host=adb-***********.**.azuredatabricks.net;Port=443;HTTPPath=sql/protocolv1/o/*********/****-*******-**********;SSL=1;ThriftTransport=2;AuthMech=3;UID=token;PWD=*****;Catalog=<CATALOG-NAME>;Schema=<SCHEMA-NAME>;ProxyHost=***************;ProxyPort=****"
);
</SCHEMA-NAME></CATALOG-NAME>
If you are using interactive JMP, then configure an ODBC Connection, which you have (I think).
Then use (in JMP 18) File->Database->Data Connectors...
New Connection
This will import all your configured DSN connections, using the DSN name.
You'll want to select the DSN name and then select New.
(This will create a new Connector based on this one)
You'll want to make sure that
Catalog=
Is in the connection field.
You'll want to Save A Copy, given a new name.
JMP 19 makes it easier to edit existing ones.
You can follow here if needed.
And... if you run into problems, give a Tech Support a call, too.