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Hello @Swathi R S - Welcome to Microsoft Q&A and thank you for reaching out with your query.
Regarding your ask, have you already reviewed the option to export to excel from the Application insights --> Logs . However the export format in excel is not JSON form, you might have to do some customization on excel data to make that happen.
However specifically if you need in JSON form , the events you see in the Application Insights portal can be exported to storage in JSON format. From there, you can download your data and write whatever code/format you need to process it.
Also for additional details on exporting telemetry from Application Insights, please refer to this documentation. Let us know if you have any further queries.