ESP32 Forum

Good afternoon!

Is it possible in ESP-32 to limit the number of WiFi connections to one? That is, only one client can connect to the ESP-32 AP. And if possible, is it possible to always issue the same IP address to the client, regardless of its mac address?

Yes & yes (it is software after all).

Suggest that you look at wifi_config_t & esp_wifi_set_config() for maximum stations.
Next you want the same IP address. Your best bet may be to limit the DHCP server's IP address range such that it only has one address.