China's fertility rate decreased by more in the decade before its one child policy was adopted (from 5.9 to 2.9), which is typical of what is experienced in developing countries, than it did after the policy was adopted to 1.7 by 1995. A best estimate of the incremental effect of the one child policy is that is reduced fertility by only about 0.33 relative to what it would have been due to declining fertility with economic development in any case.
But, as a study reviewed at the link explains, the natural experiment of comparing the socio-economic success of twins born under the one child policy, to singlets born under the one child policy (which was really a one birth policy and not a one child policy), shows that being a singlet rather than a twin resulted in substantial socio-economic, educational and health benefits for the children.
One way to describe this is that the economic circumstances already favored small families in China when the policy was adopted, but that the one child policy counteracted the inertia that would otherwise have been exerted by existing cultural norms about family size that had become obsolete but persisted anyway.
China is now dropping the one child policy, roughly one generation after it was adopted.
I haven't done the analysis, but my intuition is that while a one-child policy would have almost no impact on the autosomal genetic makeup of the Chinese gene pool, that it would significant reduce the proportion of low frequency Y-DNA haplogroups and mtDNA haplogroups in the population, since a one child policy insured that either the father's Y-DNA haplogroup, or the mother's mtDNA haplogroup is not passed to a couple's grandchildren. High frequency haplogroups would be retained at roughly the same proportions, but the proportion of the population with rare or unique mutations in their NRY-DNA or mtDNA should be cut roughly in half.