Running your ASP.NET Core (or other) application in Docker using SSL should not be an overwhelming task. These steps should do the trick.
Run the following steps from a Linux terminal (I used WSL or WSL2 on Windows from the Windows Terminal).
It should look something like the content below; call it my-site.conf or something like that.
[req]
default_bits       = 2048
default_keyfile    = localhost.key
distinguished_name = req_distinguished_name
req_extensions     = req_ext
x509_extensions    = v3_ca
[req_distinguished_name]
countryName                 = Country Name (2 letter code)
countryName_default         = US
stateOrProvinceName         = State or Province Name (full name)
stateOrProvinceName_default = Minnesota
localityName                = Locality Name (eg, city)
localityName_default        = Woodbury
organizationName            = Organization Name (eg, company)
organizationName_default    = KnowYourToolset
organizationalUnitName      = organizationalunit
organizationalUnitName_default = Development
commonName                  = Common Name (e.g. server FQDN or YOUR name)
commonName_default          = localhost
commonName_max              = 64
[req_ext]
subjectAltName = @alt_names
[v3_ca]
subjectAltName = @alt_names
[alt_names]
DNS.1   = localhost
DNS.2   = 127.0.0.1
The my-site.conf value is specifying the conf file you created in step 1.
Make sure to replace YourStrongPassword with something of your own choosing.
sudo openssl req -x509 -nodes -days 365 -newkey rsa:2048 -keyout my-site.key -out my-site.crt -config my-site.conf -passin pass:YourStrongPassword
Alternatively, create a CSR file if you have your own authority with a command as follows:
sudo openssl req -out my-site.csr -newkey rsa:4096 -nodes -config my-site.conf 
If you have your own authority and it's already trusted, you can skip steps 3 and 4 below.
Run the following command to create a pfx file.
You'll be prompted for the YourStrongPassword value you provided in step 2.
sudo openssl pkcs12 -export -out my-site.pfx -inkey my-site.key -in my-site.crt
This step will differ on Mac, Windows, and Linux.  Just follow the steps to import the pfx file as a trusted certificate
on your machine.
These files will set up your nginx image with your certificate files and also provide configuration that performs the SSL-based reversed proxy to your own container image.
This file defines the image that you will be using and gets your certificate files onto it.
FROM nginx:latest
COPY nginx.conf /etc/nginx/nginx.conf
COPY my-site.crt /etc/ssl/certs/my-site.crt
COPY my-site.key /etc/ssl/private/my-site.key
This file defines the configuration for nginx that the reverse proxy will use.
A couple of key points on this file:
- The server_namevalue should be the FQDN / DNS name you provided for the common name in your my-site.conf above (e.g. www.mycoolapi.com)
- The reverse proxy defined here will be listening on port 80 and port 443 - if you want to change that tweak the listenlines below
- It does upgrades from http/80 to https/443
- The upstream web-apidefined is used ONLY in this file, but it referencesserver api:5000- this will need to be defined in adocker-composefile that you create (see next step)
- You can define multiple servers here - if you have an API, a UI, an IdentityServer, or whatever, this reverse proxy can serve them all.  You need multiple upstreamsections and multipleserversections to define them.
worker_processes 1;
events { worker_connections 1024; }
http {
    sendfile on;
    large_client_header_buffers 4 32k;
    upstream web-api {
        server api:5000;
    }
    server {
        listen 80;
        server_name my-site;
        location / {
            return 301 https://$host$request_uri;
        }
    }
    server {
        listen 443 ssl;
        server_name my-site;
        ssl_certificate /etc/ssl/certs/my-site.crt;
        ssl_certificate_key /etc/ssl/private/my-site.key;
        location / {
            proxy_pass         http://web-api;
            proxy_redirect     off;
            proxy_http_version 1.1;
            proxy_cache_bypass $http_upgrade;
            proxy_set_header   Upgrade $http_upgrade;
            proxy_set_header   Connection keep-alive;
            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 $scheme;
            proxy_set_header   X-Forwarded-Host $server_name;
            proxy_buffer_size           128k;
            proxy_buffers               4 256k;
            proxy_busy_buffers_size     256k;
        }
    }
}
This file references your Dockerfile(s) for the various projects you have created.
The reverseproxy should point to the nginx.Dockerfile you created above.  The ports for that should match the listen values from the nginx.conf file you created.
The api should be named consistently with the server value for the upstream setting in the nginx.conf file and should expose
the same port.  MyWebApiProject is your project name or directory name for where the API (or whatever) Dockerfile is.
version: '3.7'
services:
  reverseproxy:
    build:
      context: .
      dockerfile: nginx/nginx.Dockerfile
    ports:
      - "443:443" 
      - "80:80" 
    restart: always
  api:
    depends_on:
      - reverseproxy 
    build:
      context: .
      dockerfile: MyWebApiProject/Dockerfile
    environment:
      - ASPNETCORE_URLS=http://*:5000      
    ports:
      - "5000:5000"  
    restart: always
These would just be records that alias 127.0.0.1 (localhost) to the DNS name you provided in your my-site.conf file above.