It's working fine for me, getting an API 404 response from that url

Yes, it's working fine in another device.

But in current device, it's showing the site can't be reached.

And there are no errors in the deploy logs as well.

Unable to figure the cause for this issue

Maybe something on your device is blocking it for some reason, nothing Railway can do about that unfortunately

It looks like your Public Domain is working correctly: https://bil-api.up.railway.app/

I'm getting a 404, which means that your webapp's root isn't configured correctly. You'll have to go take a look at that and fix that in your application. But you're definitely serving traffic.