sudo apt install -y mosquitto mosquitto-clients

sudo systemctl enable mosquitto.service

mosquitto -v

Mosquitto Broker Enable Remote Access (Authentication: user and password)
You can add a user/password authentication to your MQTT broker.

1) Run the following command, but replace YOUR_USERNAME with the username you want to use:

sudo mosquitto_passwd -c /etc/mosquitto/passwd YOUR_USERNAME

I’ll be using the MQTT user petermark, so I run the command as follows:

sudo mosquitto_passwd -c /etc/mosquitto/passwd petermark

sudo nano /etc/mosquitto/mosquitto.conf

# Place your local configuration in /etc/mosquitto/conf.d/
#
# A full description of the configuration file is at
# /usr/share/doc/mosquitto/examples/mosquitto.conf.example

per_listener_settings true 

pid_file /run/mosquitto/mosquitto.pid

persistence true
persistence_location /var/lib/mosquitto/

log_dest file /var/log/mosquitto/mosquitto.log

include_dir /etc/mosquitto/conf.d
allow_anonymous false 
listener 1883  
password_file /etc/mosquitto/passwd

sudo systemctl restart mosquitto

sudo systemctl status mosquitto

How to test:

mosquitto_sub -d -t testTopic -u user -P pass

mosquitto_pub -d -t testTopic -m "Hello world!"