How do I create a python 3 service that uses socket with systemd?

Here is ready to go simple shell deploy commands for your case, you can change directories, name, description of service or script and so on, description is below:

Make directory and script itself

mkdir /usr/src/python-socket -p

cat > /usr/src/python-socket/python-socket.py << 'EOL'
import socket 
host = '127.0.0.1'
port = 9999
BUFFER_SIZE = 1024 

with socket.socket(socket.AF_INET, socket.SOCK_STREAM) as socket_tcp:
    socket_tcp.bind((host, port)) 
    socket_tcp.listen(5) # Esperamos la conexión del cliente 
    conn, addr = socket_tcp.accept() # Establecemos la conexión con el cliente 
    with conn:
        print('[*] Conexión establecida') 
        while True:
            # Recibimos bytes, convertimos en str
            data = conn.recv(BUFFER_SIZE)
            # Verificamos que hemos recibido datos
            if not data:
                break
            else:
                print('[*] Datos recibidos: {}'.format(data.decode('utf-8'))) 
            conn.send(data) # Hacemos echo convirtiendo de nuevo a bytes
EOL

Set up variables for create systemd service

SERVICE_NAME=python-socket
SERVICE_DESCRIPTION="Test python service"
SERVICE_COMMAND="/usr/bin/python3 /usr/src/python-socket/python-socket.py"
SERVICE_WORK_DIR=/usr/src/python-socket/
SERVICE_USER=root

Deploy systemd service config

cat > /etc/systemd/system/${SERVICE_NAME}.service << EOL
[Unit]
Description=${SERVICE_DESCRIPTION}
After=multi-user.target

[Service]
Environment="FROM=SYSTEMD"
WorkingDirectory=${SERVICE_WORK_DIR}
Type=simple
User=${SERVICE_USER}
ExecStart=${SERVICE_COMMAND}
RemainAfterExit=no
Restart=always
RestartSec=2
StartLimitBurst=999999
StartLimitInterval=0
KillMode=process

[Install]
WantedBy=multi-user.target
EOL

Apply new service, start it and check

systemctl daemon-reload
systemctl enable ${SERVICE_NAME}
systemctl stop ${SERVICE_NAME}
systemctl start ${SERVICE_NAME}
systemctl status ${SERVICE_NAME}

As a result your systemd service config will looks like

[Unit]
Description=Test python service
After=multi-user.target

[Service]
Environment="FROM=SYSTEMD"
WorkingDirectory=/usr/src/python-socket/
Type=simple
User=root
ExecStart=/usr/bin/python3 /usr/src/python-socket/python-socket.py
RemainAfterExit=no
Restart=always
RestartSec=2
StartLimitBurst=999999
StartLimitInterval=0
KillMode=process

[Install]
WantedBy=multi-user.target

Where:

Environment="FROM=SYSTEMD" - some env variable if you want pass to your python script

Type=simple - simple systemd service it will work while script is up

RemainAfterExit=no
Restart=always
RestartSec=2
StartLimitBurst=999999
StartLimitInterval=0

These parameters will not allow your script being down in any conditions it will start on fail continiously

KillMode=process - This is how your script will stop, if you have not special SIG events in your python script it is universal