listening-port=3478
tls-listening-port=5349
alt-listening-port=80
alt-tls-listening-port=443
listening-ip=10.10.8.137
relay-ip=10.10.8.137
external-ip=<PUBLIC IP>
realm=turnstun.example.com
server-name=turnstun.example.com
fingerprint
lt-cred-mech
userdb=/var/lib/turn/turndb
total-quota=100
stale-nonce
#SSL
cert=/etc/letsencrypt/live/turnstun.example.com/fullchain.pem
pkey=/etc/letsencrypt/live/turnstun.example.com/privkey.pem
cipher-list="ECDH+AESGCM:DH+AESGCM:ECDH+AES256:DH+AES256:ECDH+AES128:DH+AES:ECDH+3DES:DH+3DES:RSA+AES:RSA+3DES:!ADH:!AECDH:!MD5"
dh2066
no-tlsv1
no-tlsv1_1
no-loopback-peers
no-multicast-peers
log-file=/var/log/coturn.log
In my config I want the server to listen on four ports 80,443,3478 and 5349. But its not listening on alternate ports and my question is if I add an extra public IP to my instance will be listening on both external IP's on all four ports.
Which user right you run coturn? Does this user has right to listen n a well known port range ( <1024)?

It is running as root.
Also the config is changed to for listening on 80 and 433 as primary and 3478, 5349 as alternative after adding a extra public ip in AWS. Even still its only listening in primary not alternative.
listening-port=80
alt-listening-port=3478
tls-listening-port=443
alt-tls-listening-port=5349
listening-ip=10.10.8.137
listening-ip=10.10.8.146
relay-ip=10.10.8.137
external-ip=<PUBLIC IP>
realm=turnstun.example.com
server-name=turnstun.example.com
fingerprint
lt-cred-mech
userdb=/var/lib/turn/turndb
#use-auth-secret
#static-auth-secret=a5b78c0a10af34d357dc2196dd8afc205a40d4743b6ff865300e74d69f11a5d7
total-quota=100
stale-nonce
#SSL
cert=/etc/letsencrypt/live/turnstun.example.com/fullchain.pem
pkey=/etc/letsencrypt/live/turnstun.example.com/privkey.pem
cipher-list="ECDH+AESGCM:DH+AESGCM:ECDH+AES256:DH+AES256:ECDH+AES128:DH+AES:ECDH+3DES:DH+3DES:RSA+AES:RSA+3DES:!ADH:!AECDH:!MD5"
#dh2066
#no-tlsv1
#no-tlsv1_1
no-loopback-peers
no-multicast-peers
#log-file=/var/log/coturn.log
verbose


@misi Thanks for replying and caring for a stranger. I just read the documentation again in clear head and found that I needed to add the below snippet to make it listen in alternate ports. I hope it helps someone.
listening-port=80
alt-listening-port=3478
tls-listening-port=443
alt-tls-listening-port=5349
listening-ip=<PRIVATE IP 1>
listening-ip=<PRIVATE IP 2>
relay-ip=10.10.8.137
external-ip=<PUBLIC IP 1>/<PRIVATE IP 1>
external-ip=<PUBLIC IP 2>/<PRIVATE IP 2>
realm=turnstun.example.com
server-name=turnstun.example.com
fingerprint
lt-cred-mech
userdb=/var/lib/turn/turndb
total-quota=100
stale-nonce
#SSL
cert=/etc/letsencrypt/live/turnstun.example.com/fullchain.pem
pkey=/etc/letsencrypt/live/turnstun.example.com/privkey.pem
cipher-list="ECDH+AESGCM:DH+AESGCM:ECDH+AES256:DH+AES256:ECDH+AES128:DH+AES:ECDH+3DES:DH+3DES:RSA+AES:RSA+3DES:!ADH:!AECDH:!MD5"
#dh2066
#no-tlsv1
#no-tlsv1_1
no-loopback-peers
no-multicast-peers
#log-file=/var/log/coturn.log
verbose
Ports listening as expected

Most helpful comment
Which user right you run coturn? Does this user has right to listen n a well known port range ( <1024)?