I need to search the issue based on linkedissue details , but it looks like we need paid app to achieve that .
I am look for an alternate option for that, is it possible to write our own function and include it in filter to search the issue based on linkedissue details ?
On Cloud, no, you can't add your own JQL functions directly. You can however write apps that can effectively emulate them, and that's what the apps you've found are doing.
You know that as an Adaptavist, I am obliged to mention the stuff Scriptrunner can do with JQL if you do decide to look at paid options - https://scriptrunner-docs.connect.adaptavist.com/jiracloud/jql-aliases.html (If nothing else, that shows you what is possible if you're happy to code for yourself)
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