Yes, particles can indeed exist to carry both energy and charge. In fact, there are fundamental particles in the Standard Model of particle physics that carry both energy and electric charge.
The most familiar example is the photon, which is the particle associated with electromagnetic interactions. Photons are massless particles that carry energy and have an electric charge of zero. They mediate the electromagnetic force and are responsible for transmitting electromagnetic radiation, including visible light, radio waves, and X-rays.
Additionally, other particles in the Standard Model, such as the W and Z bosons, also carry energy and electric charge. The W and Z bosons are responsible for mediating the weak nuclear force, which is involved in processes like radioactive decay. These bosons have non-zero masses and carry electric charges as well.
It is worth noting that the concept of charge is specific to electromagnetic interactions, and other fundamental forces, such as the strong nuclear force and the weak nuclear force, have their own associated charges (e.g., color charge in the case of the strong force). Therefore, particles that carry energy and charge can vary depending on the specific force or interaction being considered.