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I'm making a simple AND gate array out of 2n2222 transistors. Here is one cell:

^{simulate this circuit – Schematic created using CircuitLab}

When Input "A", is disabled, and "B" is still on:

^{simulate this circuit}

current flows from the base to the emitter of the transistor which is still on.

How do I filter out the smaller current when just the base-emitter on B is conducting, so the circuit functions like an AND gate? I've tried using larger resistors, and that solves the problem for a single gate. But the problem still exists when the gates are attached together.

Edit: Placing the LED in front of the AND gate solves the problem for a single gate too. But for an array of gates, this solution doesn't work.

current flows from the base to the emitter of the transistor which is
still on.

How do I filter out the smaller current when just the base-emitter on
B is conducting, so the circuit functions like an AND gate?

You should understand the emitter current equals the base current plus the collector current (Ie = Ic + Ib). If you do not want the base current ("smaller current") then place the load on the collector side of the top transistor.

^{simulate this circuit – Schematic created using CircuitLab}

This is just a note on your AND gate design. You can use CircuitLab's simulator to help understand your circuit.

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1. The simulator needs a circuit GND as a reference for its calculations. I've added it to supply negative which is the usual location.

Figure 2. The original circuit.

With the addition of some nodes for voltage measurement the DC Solver shows us that when both transistors are on that the most current through the LED will be about 0.4 mA. This is mostly due to the voltage drop across R1. You can add in another node on the LED to check what voltage it is seeing.

Note the voltage drops between NODE1, NODE4 and NODE5.

Figure 3. R1 has been reduced to 100 Ω.

Now, at least, we get 7 mA through the LED and it should be good and bright.

Notice that there is a significant voltage drop on each transistor of about 0.7 V each. You have only 2.5 V on your output. You should be able to see that this isn't going to scale well for a 3 or 4-input AND gate.

You can experiment with the simulator in your schematics to understand further what happens when you disconnect one of the inputs. Don't forget to add a GND.

At least one of the other answers has pointed out that the load should be in the collector side of Q1. The reason is that the transistors can be driven into saturation and the voltage drop across each is very low.

Figure 3. Low-side switching results in much lower voltage drop across the transistors.