Unless you've been living under a rock for a while, you've seen a good portion of these cards. The Dogmatikas. The bane of any extra deck-focused deck, which, when combined with Shaddolls and Invoked, forms a disgustingly powerful control deck. That's not what we're doing today. Today is all about the deck in its purest form.
The Dogmatikas are all about their crusade against the extra deck, so we'll barely ever use ours. I say barely because Dogmatikas cannot go first on their own. The best you can do is normal summon Ecclesia or Adin and set some traps to live until your next turn. Because of this, we're running Instant Fusion to summon out Millennium-Eyes Restrict which can be linked off into Linkuriboh to fulfil the conditions for every single summon except for Nexus and White Knight. However, Instant Fusion is currently sitting at 1, so you're rarely going to draw it in your opening hand. To fix this glaring issue, you can substitute Retort Fusion and use Kamionwizard to summon Magistus Maiden Artemis instead of the Linkuriboh play. You can also use Darkfire Dragon and summon out Striker Dragon to pretend you're doing a dragon link combo. Just be aware that the TCG doesn't exactly have this card yet, so if you get your hands on a playset of Retort Fusion and use it at an official tournament, you're gonna be disqualified.
So now, we come to the extra deck. As with all Dogmatika builds, you need to be careful about which cards you're dumping from your extra deck throughout your turn. N'tss is a non-OPT pop anything on the field so only send this when you have stuff to pop. Fossil Warrior Skull Knight is your extra copies of N'tss, but it comes with an upside. If you've already popped all the troublesome monsters on your opponent's field, he can just sit in grave until you're ready to use him. The goodest of bois. Titaniklad is pretty self-explanatory. He gives you a free summon from deck in the end phase (or a free search if you'd rather have that), but this effect is a hard OPT so you can't just dump 3 Titaniklad and build a board like that. Wind Pemasus @Ignister strikes fear into your opponent's heart as they constantly fear its effect to shuffl one of their monsters into the deck after they destroy one of yours. And finally, Herald of the Arc Light. Unlike every single synchro deck in recent memory, we only care about its ritual spell/monster search effect. This gets you White Knight who can dump Titaniklad using Dogmatikalamity to summon itself from hand.
Now it's time for the main deck. Most of these cards should be familiar. Ecclesia searches your archetype, Maximus sends 2 cards from both extra decks to grave, Fleurdelis boosts attack when your cards declare attacks and negates a monster's effects if you have another Dogmatika on field, Nadir Servant is the single-most busted search card in the game, and Punishment sends a card from your extra deck to the GY to destroy and opponent's monster as long as the attack is greater than that opponent's monster. As for the cards that you might not know, Adin is a free summon from hand that can float into any Dogmatika from deck (except Nexus and White Knight of course). White Knight lets you send a card from both extra decks to the GY when your opponent activates an effect. Ashiyan summons itself when an extra deck summon is sent to the GY and even adds a Dogmatika from grave back to hand as consolation. Nexus is your win condition. Lightning Storm on attack declaration and burns if it killed any extra deck monsters by the effect. Not to mention its amazing summon condition that lets you empty your opponents GY of extra deck monsters to summon itself.
As for spell cards, Called By is for handtrap insurance, Dwimmered Path adds any Dogmatika from GY to hand, Dogmatika Nation provides some protection to your Dogmatikas, and Dogmatikacism gives you some way to lower an opponent's monster's attack and gives you a free extra deck dump when that monster is destroyed. Handtraps are handtraps, and you can sub out the ones I used for whichever fit the scene you're in. Same with the handtraps in the side deck. As for the 3 extra deck monsters in the side deck, you can sub these in if you refuse to give in to the temptation of the extra deck. Omega recurs resources, Link God is the biggest technically-summonable send for Punishment, and the third Fossil Warrior is like the other 2 Fossil Warriors, but he's actually happy to be here.
There's quite a few other options you can run in the deck if you want to. Almiraj helps with that whole "you have almost zero way to set up a board first turn" by using Adin as its link material. Mega Zaborg can dump 8 cards from both extra decks on summon, but like all Monarchs, he tends to brick your hands more often than not. Theo is bad. But he's also a Dogmatika if you really want the whole church present. Just don't play more than one. Dogmatika Encounter and Genesis are also quite bad. But if you run into an issue known as "my opponent refuses to summon from the extra deck", Encounter can help get your monsters on field. Genesis is still really situational though, so only run that if you know you'll be able to fulfil its activation requirements consistently. Kaijus and their like do what they've always done and eat your opponent's boss monsters before they become an issue. Lightning Storm is Lightning Storm and since you're almost always going second, it can help deal with backrow decks. Forbidden Droplets is even more insurance against your opponent's bunguses. If you lack any integrity, Rivalry of Warlords, Gozen Match, and Secret Village of the Spellcasters can also be played. But in that case, why not just play the Invoked Shaddoll heresy deck instead.