Dear Please see my topology diagram attached… I am running PPPOE and DHCP server on 2 interfaces on MKT-1. After long distance my Both LAN links are close together and I have configured MKT-2 and MKT-3 (Both in Bridge Mode) on both LAN segment and attached MKT2- and MKT-3 via a switch.
In case of Single LAN Bridge port become 1 as designated and other as backup while in this scenario both ports remain designated in root bridge MKT while in other MKT one become root port
I want to create redundancy if my LAN1 segment fails, disconnected segment should be connected through LAN 2 to my main router MKT-1.. Currently i have disabled bridge port which connects to MKT3 on other LAN segment. Please help me in this regard

easy to solve using routing protocols like ospf

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Dear i would appreciate if you guide me in details
how pppoe client will reach to MKT-1 for authentication ?

Thing is, both pppoe and dhcp clients will find the server by broadcast packets. The way you have created the network, if the two routerboards have arp=proxy-arp in their bridge interface, means that every device is in the same broadcast domain. So every device will find either server 1 or server 2 on the core router, depending on which responds first. You don't need any extra config if all you want is clients find the server.

Dear Understood,
But here i want the link between router boards as a backup link...
if any of one routerboard disconnected from the core router due to cable or any switch fault...
It should be connected via 2nd RouterBoard..

Dear Understood,
But here i want the link between router boards as a backup link...
if any of one routerboard disconnected from the core router due to cable or any switch fault...
It should be connected via 2nd RouterBoard..

then you should read about link failover using ospf

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Dear Understood,
But here i want the link between router boards as a backup link...
if any of one routerboard disconnected from the core router due to cable or any switch fault...
It should be connected via 2nd RouterBoard..

Make 2 vlan from R1, then add them to bridge as backup link ?