These claims originate with a paper by a mathematician named Valentina Zharkova and others, who studied a correlation between solar magnetic fields and sunspots. Based on the last three solar cycles, her model predicted that the next several solar cycles will be less intense than typical (i.e. fewer sunspots), which implies lower radiant output.
Here is an article addressing the claims and explaining why it's not something to worry about. Some key points include:
The paper only addresses solar activity, and does not mention the impact that lower solar radiation would have on earth. Climate scientists have looked at the impact that a Maunder Minimum would have, and found that the cooling effect of reduced solar output is less than the warming effect of increased greenhouse gases, so the net effect is that the earth will continue to warm even if the predictions turn out to be correct.
The cooling associated with the Maunder Minimum was not entirely due to the lower sunspot numbers. There is evidence that massive volcanic eruptions played a significant role in the cooling.
Claims that the earth is already cooling because there may be fewer sunspots 5 or 15 years from now simply make no sense, and global temperature measurements clearly show that there is not a cooling trend.