Caddy is a really nice modern web sever written in Go, with an awesome feature of automatic generation and renewal of HTTPS certificates. To run Caddy in Docker for serving a static website (with HTTPS enabled), do as instructed in the documentation on Docker Hub:

docker run -d --cap-add=NET_ADMIN -p 80:80 -p 443:443 -p 443:443/udp \
    -v static_site_root_dir:/srv \
    -v caddy_data:/data \
    -v caddy_config:/config \
    caddy caddy file-server --domain mydomain.com

As such, you are just managing the files in static_site_root_dir (which is mapped to to the container’s /srv directory), with the container’s /data and /srv directories mounted as Docker volumes.

The --cap-add=NET_ADMIN option improves performance of the UDP-based HTTP/3 protocol (enabled in Caddy by default) by increasing the buffer size for the sockets.