Unfortunately those cars are well known for electrical gremlins. Your best bet is probably to just get rid of it and cut your losses instead of throwing good money after bad at it.

The injectors/fuel pump can't run with the KEY OFF unless the ASD relay's coil  (Automatic Shutdown Relay) is being energized (ignition switch Power to pin socket 85 and "PCM provided Ground" to pin 86 of the relay's coil)

Or if the relay is broken. (relay switch stuck closed).

Let's look at what it takes for the "fuel pump/injectors" to run 1st, and then try to determine why it's happening during "KEY OFF".

The ASD relay supplies power to the vehicle’s ignition coils, fuel pump, and fuel injectors, as well as telling the PCM to output voltage signals to other control modules/components.

The Ignition Switch provides Power to the ASD Relay at socket 85 and the computer controls the Ground Circuit side of it at pin socket 86. When the computer provides "Ground Signal" to socket pin 86, it completes the relay's coil circuit (KEY ON), energizes the relay's coil, closes the internal switch between sockets 87 and 30, which provides power to the fuel system's electrical components and the ignition coil circuit.

Let's have a "look see" just so we're all on "the same page"

KEY OFF the relay looks like this.

KEY ON the relay looks like this.

So, is there a "demonic possession" happening at pin socket 86 providing Ground during KEY OFF?

(unlikely because the power side of the relay's coil (Pin socket 85) is "switched" (KEY ON) from the ignition.

You'd have to have two "demons". One providing power to socket 85 (during KEY OFF) and another providing Ground (through a PCM command or a wiring short) to socket 86 ( during KEY OFF)

If that's the case you'd want to begin your "exorcism" at the ignition switch because the relay and the computer think the KEY is in the ON position.

But you already did that when you replaced the ignition switch. So, could the problem be in the ignition switch connector or wiring?

Then you even replaced the TIPM (Totally Integrated Power Module)  and I assume you didn't use your old ASD relay in the new unit. (did you?)

If you did, swap it with another 40 amp relay in the box.

Is this just a broken ASD relay that's staying Closed after the Key is turned OFF or is the relay's coil sockets receiving both Power and Ground during KEY OFF?

After you confirm it isn't a defective ASD relay, check if the ASD relay socket pin 86 is Grounded when the KEY is in the OFF position AND relay socket pin 85 is getting Power when the KEY is in the Off position.

(they shouldn't be).

It sounds like they are and that's an issue in the ignition switch connector/wiring (somewhere in the circuit).

I Know, I took the "long way around" but it helps to "talk it out" and although it's informative it MAY or NOT BE  relevant because

you have a "side symptom" which has to be considered.

The radio comes on by itself during KEY OFF.

Typically, when the ignition is "turned off" with the radio on,

when the ignition is turned back on, the radio comes back on.

Your radio is coming on in "KEY OFF" and your ASD relay's coil seems to be receiving "ignition switch" power and  "PCM Ground" with the "KEY OFF". (unless the ASD relay is defective and stuck closed)

Is that too much of a coincidence to be ignored or is the PCM sending an "ignition ON" output signal to a control module that controls radio power because the ASD relay is stuck CLOSED?

Frankly, you've done all you can in "parts bombing" this issue. (assuming you replaced that ASD relay). New ignition switch, new TIPM, new fuses, new battery.

You've put out considerable cash in parts , and assuming you've replaced the ASD relay, it's time to invest $30 in a 1 year subscription to ALL DATA DIY for that 2015 Jeep Patriot

You need to closely examine the ignition switch circuit, its wiring and connectors to figure out how the PCM, and the ASD Relay (which should be OFF in "KEY OFF"), are getting "KEY ON" voltage with the Brand New ignition switch in the KEY OFF position.

In the case of that ASD Relay alone, the only leg of the circuit that should have power during KEY OFF is the Blue traced circuit.

Everything in Red shouldn't have power (KEY OFF) and the PCM shouldn't be providing Ground (Green) in KEY OFF.

Yet that 40 amp ASD relay is Closed and has power ON during KEY OFF.

Look at the PCM "ASD Control" Outputs too. Aside from your electronic fuel system components and your ignition coils being powered, the PCM is turning on a lot of other stuff when the ASD Relay is closed.

No wonder your battery is draining

Billybob is right about Jeep's infamous problems with electrical gremlins. You'll need to find a mechanic who will pull up schematics and test the relays, power/ground, etc.

You also might want to take a look at the TSBs for this year and model at carcomplaints.com.

And, it might be useful to go here: https://www.jeeppatriot.com

No I can’t return it it was sold as is no warranty kind of a crappy deal but honestly love the car just need the possession to stop