MCU - Two power input: from PoE and DC 12V Switch between them
The simplest incarnation of a power selector is two low-forward-voltage-drop Schottky diodes:



simulate this circuit &ndash; Schematic created using CircuitLab
This will not do anything &quot;intelligent&quot; - it will roughly do what you asked originally, which is to pass the highest of the two input supply voltages to the power rail of the board. If you need anything more complicated you're probably going to need either integrated or discrete high-side switches, but there's not enough detail in your requirements to say whether that's needed. You're going to need to figure out:

How much current can the POE and PSU inputs provide at most?
How much current will the 12V input draw at most?
Does the board have (any, or enough) over-voltage and/or over-current and/or TVS protection for your application?
Does the board have enough filtration for your application?
Do you need fusing?
What, if any, specific behaviour do you want to happen on brownouts and switches in either direction?