Outstanding problems for MOND
The most serious problem facing Milgrom's law is that it cannot completely eliminate the need for dark matter in all astrophysical systems: galaxy clusters show a residual mass discrepancy even when analysed using MOND.
[2] The fact that some form of unseen mass must exist in these systems detracts from the elegance of MOND as a solution to the missing mass problem, although the amount of extra mass required is 5 times less than in a Newtonian analysis, and there is no requirement that the missing mass be non-baryonic. It has been speculated that 2 eV neutrinos could account for the cluster observations in MOND while preserving the theory's successes at the galaxy scale.
[45][46] Indeed, analysis of sharp lensing data for the galaxy cluster Abell 1689 shows that MOND only becomes distinctive at Mpc distance from the center, so that Zwicky's conundrum remains
[47], and 1.8 eV neutrinos are needed in clusters.
[48]
The 2006 observation of a pair of colliding galaxy clusters known as the "
Bullet Cluster",
[49] poses a significant challenge for all theories proposing a modified gravity solution to the missing mass problem, including MOND. Astronomers measured the distribution of stellar and gas mass in the clusters using
visible and
X-ray light, respectively, and in addition mapped the inferred dark matter density using gravitational lensing. In MOND, one would expect the missing mass (which is only apparent since it results from using Newtonian as opposed to MONDian dynamics) to be centred on the visible mass. In ΛCDM, on the other hand, one would expect the dark matter to be significantly offset from the visible mass because the halos of the two colliding clusters would pass through each other (assuming, as is conventional, that dark matter is collisionless), whilst the cluster gas would interact and end up at the centre. An offset is clearly seen in the observations. It has been suggested, however, that MOND-based models may be able to generate such an offset in strongly non-spherically-symmetric systems, such as the Bullet Cluster.
[50]
Several other studies have noted observational difficulties with MOND. For example, it has been claimed that MOND offers a poor fit to the velocity dispersion profile of
globular clusters and the temperature profile of galaxy clusters,
[51][52] that different values of a0 are required for agreement with different galaxies' rotation curves,
[53] and that MOND is naturally unsuited to forming the basis of a theory of cosmology.
[54] Furthermore, many versions of MOND predict that the speed of light be different from the speed of gravity, but in 2017 the speed of gravitational waves was measured to be equal to the speed of light.
[4]
Besides these observational issues, MOND and its generalisations are plagued by theoretical difficulties.
[54][55] Several ad-hoc and inelegant additions to general relativity are required to create a theory with a non-Newtonian non-relativistic limit, the plethora of different versions of the theory offer diverging predictions in simple physical situations and thus make it difficult to test the framework conclusively, and some formulations (most prominently those based on modified inertia) have long suffered from poor compatibility with cherished physical principles such as conservation laws.
Source:
https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
Is your theory can explain these ? How your theory is different from MOND ? Since you are asked this question you are not in academy ( I highly suppose) Hence I am not sure that your theory can solve Dark matter problem.