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Black hole is an object with a strong gravitational interaction where classically no particles even light can escape from it. The spacetime of a black hole is described by a metric satisfying the Einsteins equation under the general relativity. A simple solution of the Einsteins equation for a black hole system yields inevitable singularities at $r=0$ and $r=2M$ on the spacetime. Such singularities are difficult to explain through physics laws. A metric function, denoted by $f(r)$, was introduced to generalize some well-known solutions such as the Schwarzschild and Reissner-Nordstr"om metrics, which leads to other possible solutions, including regular black holes. The Reissner-Nordstr"om is a charged black hole where its potential leads to a metric function depending only on radius $r$. Regarding this concept, we propose a black hole system with magnetic charge whose magnitude and direction resemble Earths magnetic field. Thus, it is necessary to extend the metric function to $f(r, heta)$, since we use a model of the Earths magnetic field where the magnetic potential depends on the polar angle $ heta$. We present a search for this new type of regular black holes and there might be possibility to generalize to a class of black holes with a metric function $f(r, heta)$.