That's not a "P", that's a Chi and a Rho.
According to the historian Eusebius, Constantine received a heavenly vision while praying.
[W]hile he was thus praying … a most marvelous sign appeared to him from heaven … when the day was already beginning to decline, he saw with his own eyes the trophy of a cross of light in the heavens, above the sun, and bearing the inscription, CONQUER BY THIS [In hoc signo vinces, “with this symbol you shall prevail”]. At this sight he himself was struck with amazement, and his whole army also, which followed him on this expedition, and witnessed the miracle.
https://aleteia.org/2017/07/28/the-miraculous-story-behind-the-chi-rho-symbol/
Long story short, Constantine's dream led him to boost his soldier's morale with a red cross painted on their shields in line with this "dream" of victory he said he received.
A red cross on a shield.
A rot kreutz on a schild.
And now you know where the Rothschilds got their name from.