Hi Angelos, thank you for your feedback.
I had auto-assign Public IP enabled to access to each the Fargate instances whenever required. Having it enabled will assign a public IP address to each task i.e. Fargate instance and I can access to backend application using assigned public IP and port.
Incase we have it disabled, we would need to setup private subnet or NAT gateway as mentioned in aws documentation. https://docs.aws.amazon.com/AmazonECS/latest/developerguide/service-configure-network.html
I hope I could be helpful and answered correctly to your question. Please let me know incase of any concerns or questions.
Regards