Is there a way by which we can allow https calls from only aws servers from across another region without VPC peering?

I am a newbie to AWS. I created two instances in two different regions. One was Windows and the other was Linux. Both had public ips. I logged onto windows via Remote Desktop protocol and successfully tested the html page on linux instance. So I was able to make successful html calls.

As per the other answer, instances can communicate using public/elastic IP addresses which means that VPC or Transit Gateway peering isn't required.

Security groups are definitely the best way to limit communications between the instances. When you say "that will not work" - what isn't working?

See Amazon VPC-to-Amazon VPC connectivity options.