How to Install Realtek RTL8168 Driver on Debian Gnu/Linux Distro
GNU/Linux Debian Realtek rtl8168 Driver Setup Guide
How to Install Realtek RTL8168x Ethernet Controller Driver on Debian GNU/Linux Distribution.
This Realtek r8168 Driver Debian Setup should support All the following PCI Express 10/100/1000M Gigabit Ethernet Adapters:
- RTL8168B/8111B
 - RTL8168C/8111C
 - RTL8168CP/8111CP
 - RTL8168D/8111D
 - RTL8168DP/8111DP
 - RTL8168E/8111E
 - RTL8111G/8111H
 - RTL8411/8411B
 
And again also the PCI Express 10/100M Fast Ethernet Interfaces:
- RTL8101E
 - RTL8102E
 - RTL8103E
 - RTL8105E
 - RTL8106E
 - RTL8107E
 - RTL8401
 - RTL8402
 
Please be aware of how this Driver is Not supporting all the Linux Kernels range, so in case of issue consult the available Online Documentation.
So as a possible Solution, then you may also see: How to Install New Kernel Guide.
Again, in case of Issue for preventing any possible Driver loading Interference you should also take into account: How to Blacklist Kernel Modules.