Input is 12V, output I need is 12.6V with 1Amps current limit.
Output connected: Lithium battery 8.1V to 12.6V range and a resistive load in parallel.

Since battery is also connected at the output, so current limit is required. Otherwise battery drains huge current, if limit is not there

 

SEPIC converter based on LM3478.
https://webench.ti.com/power-designer/switching-regulator

 

Guessing that you wish to supply a load with 12.6 v if available or if not use battery? If so might diode OR the supplies into the load. Could use a boost- buck converter ? I thought I had one but have conflicting specs.

 

You didn't state the needed voltage. For example from a 12 volt output to a 5 volt needed voltage you would use an LM7805. For a 9 volt needed voltage you would use a Lm7809. The last 2 digits reference the voltage output. These are available in both thru hole and smd.

 

I didn't mention that the supply voltage needs to be higher than the needed voltage.