Hi @angel sheela ,
Per my research, you can follow the steps to covert ASP site to sharepoint site.
Step1: Add a Web Deployment Project to your website solution that will create a single DLL for the website. This step will give us the code-behind DLL and other dependency DLLs for the website.
Step2: Copy the bin folder items (DLLs) into the SharePoint site, and tweak the web configuration file of the SharePoint site to use the copied DLLs.
Step3: Open your created SharePoint site in SharePoint Designer and import the web pages from our web application and link it to the appropriate DLLs.
For more details:
https://www.codeproject.com/Articles/21465/Converting-an-ASP-NET-site-into-a-SharePoint-site
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As far as I know, the oss search doesn't work in sharepoint online. You can use the sharepoint online default search by following document
https://learn.microsoft.com/en-us/microsoftsearch/get-started-search-in-sharepoint-online
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