Away from my books but:
... You are wielding a weapon with the Two-Handed property. As far wielding a weapon with the Two-Handed property with a shield, I'm thinking a DM isn't going to go along with that (Though it looks like the Quarterstaff is Versatile).
So is the spear now. I first heard it on a Dungeon Dudes You Tube video, about Polearm Master +Sentinel. D&D Beyond confirms also it:
https://www.dndbeyond.com/equipment/spear and
Polearm Master
When you take the Attack action and attack with only a glaive, halberd, quarterstaff, or spear, you can use a bonus action to make a melee attack with the opposite end of the weapon. This attack uses the same ability modifier as the primary attack. The weapon’s damage die for this attack is a d4, and it deals bludgeoning damage.
While you are wielding a glaive, halberd, pike, quarterstaff, or spear, other creatures provoke an opportunity attack from you when they enter your reach.
I have a Spear and Shield wielding Mountain Dwarf War Cleric 2/ Fighter Battle Master build ready for full release
The Spartan Crusader:
https://www.dndbeyond.com/profile/Merlex/characters/27043085
