Your question highlights a misunderstanding about the nature of electricity and magnetism, but that's okay! I'm an electrical engineer and the concepts are a bit baffling at times to me! Good on you for being curious and asking.
To start...electricity isn't something you just have. You can't hold electricity in your hand. The truth about electricity starts with chemistry, oddly enough:
You're aware that all matter is made of atoms, which themselves are composed of protons, neutrons, and electrons. For our discussion here, we only care about electrons, and briefly about protons. Electrons have a negative charge, and protons have a positive charge. Like charges repel, and unlike charges attract (electrons repel other electrons, protons repel other protons, and electrons and protons are attracted to each other). If you add up all of the charge of an atom and get 0 (all the positive charges cancel out all of the negative charges) then that atom is considered to be electrically neutral.1
Simply put, when you have extra electrons that move around, this creates what is called electrical current. This is what most people are talking about when using the generic term "electricity": you have electrons moving through a medium, often a metal wire, and it's performing some amount of work (turning on a light, etc.). 2
When you mention the "strength" of the electricity, that is also a concept that doesn't exactly make sense in the context of the physics involved. If you already understand potential energy, skip this paragraph: if you hold a ball at your waist and drop it, it will hit the ground with some amount of force, yes? Now if you drop from the top of your house, it will hit the ground with a greater force. Why is that? The mass of the ball has not changed, and neither did the initial speed (you're not throwing the ball in either case), so something else must have changed: speed. 395
The one ball had a longer time to accelerate, and had accumulated more of what is known as kinetic energy before imparting that energy into the ground. But that only makes sense if it had energy to start with (you can't give something that you don't have in the first place). If the ball started out as motionless, where did the energy some from? Potential energy. The ball that started off higher had greater potential energy than the one that started at your waist. As it fell, the potential energy converted into kinetic energy as the ball sped up and got closer to the ground. At the exact instant it hit the ground, it no longer had any potential energy: it's all been converted into kinetic. When it stops moving on the ground, it has neither.
The concept of potential energy can be applied to electricity as well, with a quantity known as voltage. Voltage represents the electrical potential energy difference between a particle (the ball) and a reference point (the ground). If a particle has a high voltage, that means it really wants to go to the reference point because, in general, objects in nature don't like having extra energy. 3
So what does this have to do with magnetism? As it turns out, moving electrical charges (current) create a magnetic field, which is a force field that acts on electrically charged particles. How and why are beyond the scope of this discussion and require an understanding of both physics and higher level math (lots of calculus and differential equations), but they were discovered by a guy named <PERSON>; you can google "<PERSON>'s equations" if you're curious.
Additionally, changing magnetic fields will actually induce a current! That's how electricity is generated: something (steam, wind, etc.) spins a magnet that rotates in the center of a bunch of wires, and out pops electricity.4
Theoretically speaking, I could imagine a scenario in which you could use a magnetic field to "zap" something, but I can't think of a specific real-world example off the top of my head. But suffice it to say that no, simply holding a magnet would not increase the "damage" that the electricity would do, at least not in any noticeable way.
1: https://en.wikipedia.org/wiki/Electric_charge
2: https://en.wikipedia.org/wiki/Electric_current
3: https://en.wikipedia.org/wiki/Electric_potential
4: https://en.wikipedia.org/wiki/Electromagnet 621