How to increase quota outside of the default availability zone

Amazon EC2 provides different resources that you can use. These resources include images, instances, volumes, and snapshots. When you create your AWS account, we set default quotas (also referred to as limits) on these resources on a per-Region basis.

So you manage Quotas on per-Region basis

https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/ec2-resource-limits.html

Every AZ is a physical location with it's own limits (number of hardware). Sometimes, all resources of some particular type in an AZ may be in use by other clients, so at this moment you can not get a new instance in this particular AZ

That's why it's recommended to architect system for multi-AZ allocation. If you need to guarantee the availability of a specific instances type in particular Availability zone, consider "Reserver instances"

Can apply to usage across all Availability Zones in an AWS region, or can provide a capacity reservation when assigned to a specific Availability Zone.

https://aws.amazon.com/ec2/pricing/reserved-instances/