Where can I buy or research motherboad by its I/O Connectors?

Solution
It's impossible, the best bet is if you have an e.g. ASUS then 'LOOK' at similar ASUS MOBOs. Here's the problem, you can find 2 MOBO with the same USB, NIC, Audio, etc BUT the arrangements can easily be different; there's no standard 🙁

Also, this sounds like you're trying to reuse an OEM system with a welded-on I/O. Another problem, OEM MOBO aren't always the mATX, ATX, etc standard and then the standoffs might not match-up etc. Further, buying a MOBO based upon I/O placement is well a really bad reason.

If the standoffs are indeed standardized then get a Dremel and 'grind' it off fit the new I/O that comes with the MOBO into the hole {measure 1st before cutting}or better a new case if needed.
It's impossible, the best bet is if you have an e.g. ASUS then 'LOOK' at similar ASUS MOBOs. Here's the problem, you can find 2 MOBO with the same USB, NIC, Audio, etc BUT the arrangements can easily be different; there's no standard 🙁

Also, this sounds like you're trying to reuse an OEM system with a welded-on I/O. Another problem, OEM MOBO aren't always the mATX, ATX, etc standard and then the standoffs might not match-up etc. Further, buying a MOBO based upon I/O placement is well a really bad reason.

If the standoffs are indeed standardized then get a Dremel and 'grind' it off fit the new I/O that comes with the MOBO into the hole {measure 1st before cutting}or better a new case if needed.
 
Solution
What case?
Provide the brand and model of the PC.

Only some of the consumer PC brands' models have I/O shields that are replaceable. The majority have their holes for the I/O ports punched out of the chassis' back panel itself making it completely proprietary and also because of lower manufacturing cost.