How does your HTTP (80) server block for example.com looks like? Make sure server_name is set only to example.com www.example.com. If there is _ or wildcard entry *.example.com make sure to change it to example.com www.example.com.
This is example how it should look like:

server {
    listen 80 default_server;
    listen [::]:80 default_server;
    server_name example.com www.example.com;
    return 301 https://$server_name$request_uri;
}

Setup one block that will serve some static content for sub.example.com.
You can take a look at Server blocks tutorial if it comes to help.
You can share config here so we can look at it.

I’m having the same issue.

1. Initial Server Setup with Ubuntu 16.04
    1. How to Use SSH Keys with DigitalOcean Droplets
    2. Community Post: Updating Ubuntu (14.04) -- Security Updates
2. How to Install Nginx on Ubuntu 16.04
3. How to Set Up Nginx Server Blocks on Ubuntu 16.04
4. How to Install Node.JS on Ubuntu 16.04

Installed in the following order above, all DigitalOcean articles. I’m stuck on #3 because my test subdomain keeps rerouting to https as well. I’ve combed through everything I can think of, from DNS settings to nginx.conf and sites-available/enabled and default_server.