What data of agricultural yield to use for India?
In case you cannot access official local data, I recommend the use of the IFPRI resource MapSPAM2010. 
Quoting the description of the dataset: 


  Using a variety of inputs, IFPRI's Spatial Production Allocation Model (SPAM) uses a cross-entropy approach to make plausible estimates of crop distribution within disaggregated units. Moving the data from coarser units such as countries and sub-national provinces, to finer units such as grid cells, reveals spatial patterns of crop performance, creating a global grid-scape at the confluence between geography and agricultural production systems. Improving spatial understanding of crop production systems allows policymakers and donors to better target agricultural and rural development policies and investments, increasing food security and growth with minimal environmental impacts.


The dataset makes available data about agricultural variables for 42 crops at 10km resolution for the whole world. More info are available in the MapSPAM website, while the full dataset is available here. 

Reference: International Food Policy Research Institute, 2019, "Global Spatially-Disaggregated Crop Production Statistics Data for 2010 Version 1.1", https://doi.org/10.7910/DVN/PRFF8V, Harvard Dataverse, V3 

You can download the global rasters and then clip the area you are interested in and make your own estimates regarding specific crops and production technologies.

The information in this dataset, would help you to set up a relatively simple crop model, such as the FAO AquaCrop. This system, even with a approximative calibration, could help you to understand some of the impacts of the 


  meteorological factors on the agricultural yields.