Hello,
We apologize for the issue you are facing with your search queries only returning the homepage. It sounds like there may be a setting in Rank Math that needs to be adjusted to ensure that your search results are indexed correctly.
To fix this, you can check the following settings:
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Noindex Search Results: Make sure that the search results pages are set to "noindex". You can do this by navigating to Rank Math SEO → Titles & Meta → Misc Pages in your WordPress dashboard and enabling the Noindex Search Results option. This will prevent search engines from indexing your search results pages, which might help in resolving the issue.

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Check Redirections: Ensure that there are no unwanted redirections set up that might be affecting your search functionality. You can review your redirection settings under Rank Math → Redirections.
If you continue to experience issues after checking these settings, please reply to this ticket, and a human agent from the Rank Math Support team will assist you further.
Thank you for raising this concern, and we hope to help you resolve it soon!
Sources:
Is Your Site the Victim of Internal Site Search Spam? » Rank Math
Don’t seems the advice solves the issue.
Problem seems only on mobile.
Hello,
This issue could be caused by conflicting plugins/themes on your website. Kindly make sure you are using the latest version of all the plugins and themes, please update if not yet.
Here’s a guide for troubleshooting further if the issue persists:
https://rankmath.com/kb/check-plugin-conflicts/
You can also follow the steps in this video:
https://www.youtube.com/watch?v=FcIWRhcUP2c
Only the site admin would know and your users won’t be affected by this troubleshooting.
If the issue persists, then we might need to take a closer look at the settings. Please edit the first post on this ticket and include your WordPress & FTP logins in the designated Sensitive Data section.
Please do take a complete backup of your website before sharing the information with us.

It is completely secure and only our support staff has access to that section. If you want, you can use the below plugin to generate a temporary login URL to your website and share that with us instead:
https://wordpress.org/plugins/temporary-login-without-password/
You can use the above plugin in conjunction with the WP Security Audit Log to monitor what changes our staff might make on your website (if any):
https://wordpress.org/plugins/wp-security-audit-log/
Let us know how it goes. Looking forward to helping you.
Thank you.
Hello,
Since we did not hear back from you for 15 days, we are assuming that you found the solution. We are closing this support ticket.
If you still need assistance or any other help, please feel free to open a new support ticket, and we will be more than happy to assist.
Thank you.