To enable AKS to store your pod logs, go to your AKS resource, Monitoring section, Logs. Create a workspace and enable logs.
To enable kube-apiserver logs go to your AKS Resource Group (the RG you created do deploy AKS service, not the RG that is automatically generated by AKS), Monitoring section, Diagnostic settings, click on your AKS from the list, on "Diagnostics settings" screen, click on "Add diagnostic setting".
Input a name, check "Send to Log Analytics", select you subscription and workspace, check the logs you want and click on save.
Wait a few minutes, then you query AzureDiagnostics logs:
AzureDiagnostics
| where Category == "kube-apiserver"
| project log_s