Hi, I would like to introduce a basic Captive portal on my router runs in openwrt version x... Suggest me the best solution that should work in both bridge and NAT mode in AP.
There's no such version.
Are you asking about "Captive Portal Detection" as in your title, or are you asking for recommendations for a captive portal package?
What do you mean "bridge and nat mode"?
A captive portal will always run on a router (with an upstream Internet connection) and is usually bound to the lan bridge interface on that router.
You might want to read the following: