The question pertains to the milestones and targets set by the National Framework for Malaria Elimination in India (2016-2030). Here, we're tasked with identifying the specific target that needs to be met by the year 2027. Let's evaluate each option to determine which is the correct target for 2027:

1. Entire country is to have no indigenous cases and no deaths due to malaria: This is indeed the correct answer. By 2027, the target is that no indigenous cases or deaths due to malaria should occur across the country. This is a key milestone towards achieving malaria elimination by 2030.
2. All states and UTs must establish fully functional malaria surveillance to track, investigate and respond to each case: Effective malaria surveillance is crucial, but this goal is more relevant to initial stages rather than a target fixed for 2027 specifically.
3. All states and UTs must reduce API to less than 1 case per 1000 population at risk: Achieving an Annual Parasite Incidence (API) of less than 1 case per 1000 is an intermediate goal as part of reduction efforts but not specifically pegged as a target for 2027.
4. Entire country has to initiate the process for certification of malaria elimination: Certification processes typically follow the achievement of elimination targets, which is scheduled for the final phase towards 2030.

Thus, after analyzing all the options, the specific milestone for 2027 is that the entire country is to have no indigenous cases and no deaths due to malaria. This is a critical step in the broader strategy of completely eliminating malaria by 2030.