We need to create an Stealth (DMZ, Split or Hidden Master) Name Server. We are able to create Name Server for our private network and our sub-domain's are resolve in our Local Area Network where not in World Wide! Would you please help us to resolve the missing configuration? 
Note: Sorry for being the large question, We beg your pardon as we are fresh contributor to an R&D based community.
Where following domain we have:
Domain       : chorke.org
Name Server  : ns8533.hostgator.com
Name Server  : ns8534.hostgator.com
Subdomain    : bgd.chorke.org (public)
CNAME of bgd : cki00.ddns.net (noip.com)
Network information as below:
GTW : 10.19.83.1    (Gateway/Router)
DMZ : 10.19.83.3    (bgd.chorke.org  & Name server)
LAN : 10.19.83.0/24 (Private network & range 0~255)
Following packages installed:
sudo su
apt update && apt upgrade
apt install bind9 bind9utils bind9-doc dnsutils
Startup options in /etc/default/bind9
RESOLVCONF=no
OPTIONS="-u bind -4"
Options in /etc/bind/named.conf.options
acl internals {
        127.0.0.0/24;  # 1-254
        10.19.83.0/24; # 1-254
};
acl externals {
        10.19.83.0/29;  # 1-7   (public)
        !10.19.83.0/24; # 1-254 (private)
};
options {
        directory "/var/cache/bind";
        auth-nxdomain no;
        forwarders {
                8.8.8.8;    # Google DNS
                8.8.4.4;    # Google DNS
                10.19.83.1; # Router DNS
        };
        dnssec-validation auto;
        listen-on-v6 { none; };
        listen-on port 53 {
                127.0.0.1;
                10.19.83.3;
        };
        allow-transfer { none; };
        allow-query { internals; };
        allow-recursion { internals; };
};
Zones in /etc/bind/named.conf.local
include "/etc/bind/rndc.key";
zone "bgd.chorke.org" {
    type master;
    file "/etc/bind/zones/db.bgd.chorke.org";     # forward zone
    allow-update { key rndc-key; };
};
zone "83.19.10.in-addr.arpa" {
    type master;
    file "/etc/bind/zones/db.83.19.10";           # reverse zone
    allow-update { key rndc-key; };
};
// consider adding the 1918 zones here
// include "/etc/bind/zones.rfc1918";
Forward zones in /etc/bind/zones/db.bgd.chorke.org
$TTL     600
$ORIGIN bgd.chorke.org.
@       IN      SOA     ns0.bgd.chorke.org. root.bgd.chorke.org. (
                        201908051           ; Serial       YYYYmmddI
                             3600           ; Refresh            01H
                              600           ; Retry              10M
                            86400           ; Expire             01D
                              600 )         ; Negative Cache TTL 10S
; NS Records
@       IN      NS      ns0.bgd.chorke.org.
@       IN      NS      ns8533.hostgator.com.
@       IN      NS      ns8534.hostgator.com.
@       IN      NS      bgd.chorke.org.
@       IN      A       10.19.83.3
; A  Records
apn             A       10.19.83.2
ftp             A       10.19.83.4
gtw             A       10.19.83.1
ns0             A       10.19.83.3
Reverse zones in /etc/bind/zones/db.83.19.10
$TTL     600
$ORIGIN 83.19.10.in-addr.arpa.
@       IN      SOA     ns0.bgd.chorke.org. root.bgd.chorke.org. (
                        201908051           ; Serial       YYYYmmddI
                             3600           ; Refresh            01H
                              600           ; Retry              10M
                            86400           ; Expire             01D
                              600 )         ; Negative Cache TTL 10S
; NS  Records
@       IN      NS      ns0.bgd.chorke.org.
@       IN      NS      ns8533.hostgator.com.
@       IN      NS      ns8534.hostgator.com.
@       IN      NS      bgd.chorke.org.
; PTR Records
1.83    IN      PTR     gtw.bgd.chorke.org.
2.83    IN      PTR     apn.bgd.chorke.org.
3.83    IN      PTR     ns0.bgd.chorke.org.
4.83    IN      PTR     ftp.bgd.chorke.org.