applicationDate is not available in ODATA API Data Dictionary.
How to report Application Date in ODATA API?
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To be able to use the field application date in ODATA API, you must configure the field in the application template. Here is sample configuration that can be done via Manage Template:
Once the field is added, Run an ODATA API Metadata Refresh to update the ODATA API Data Dictionary.
2365214 - The Manage Templates Tool