Nexus docker proxy behind nginx reverse proxy separate push and pull

Question

I've set up a nexus docker registry with the proxy type. And I put the registry behind an Nginx reverse proxy as follow:

file registry.example.com.conf:

upstream nexus {
    server 127.0.0.1:8080;
}

proxy_send_timeout 120;
proxy_read_timeout 300;
proxy_buffering    off;
proxy_request_buffering off;


server {
    server_name registry.example.com.conf;
    client_max_body_size 1G;
    location / {
        proxy_pass http://nexus/;
        proxy_set_header Host $host;
        proxy_set_header X-Real-IP $remote_addr;
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header X-Forwarded-Proto "https";
    }

    listen 443 ssl; # managed by Certbot
    ssl_certificate /etc/letsencrypt/live/example.com.conf/fullchain.pem; # managed by Certbot
    ssl_certificate_key /etc/letsencrypt/live/example.com.conf/privkey.pem; # managed by Certbot
    include /etc/letsencrypt/options-ssl-nginx.conf; # managed by Certbot
    ssl_dhparam /etc/letsencrypt/ssl-dhparams.pem; # managed by Certbot

}
server {
    if ($host = registry.example.com.conf) {
        return 301 https://$host$request_uri;
    } # managed by Certbot

    listen 80;
    server_name registry.example.com.conf;
    return 404; # managed by Certbot


}

For pull requests it's ok and works fine. I can pull images from registry.example.com.conf and if it does not exist, it'll pull it from the hub.docker.com. but when I want to put images to registry.example.com.conf I get:

5216338b40a7: Layer already exists 
error parsing HTTP 404 response body: unexpected end of JSON input: ""

And I think it's because of the proxy type of my registry in nexus. I should create another registry in nexus with the type of hosted I think. But its subdomain also should be different from the proxy type (ex. registry2.example.com). So when I want to push an image I shoud tage it with registry2 and when I want to pull it I should get with registry. How can I setup the nginx to support both pull and push requests of docker within the same domain? I also read this code but it is not complete and correct