I have two time series representing scores, lets call it score A - score B, score A is related to a company and it is observed every year from 1990 (about 27 observation) score B is related to a product and it is observed every quarter from 2016 I would like to check if changes in score A influence change in the score B, but I don't know where to start.
Avoiding the fine details, what you are looking for is a cross correlation. This will give you whether there's any influence (whether it be correlated or anticorrelated) and a time lag.
Keep in mind the arrow of time (effect doesn't precede a cause) and remember that correlation does not imply causality. You will want to get a large enough data set that you can perform an analysis of variation to determine how reliable your conclusion is.
As your data set for B is miniscule, I would seriously doubt any meaningful conclusions can be drawn. When it comes to statistics, as Stalin has ashamedly said in his approach to warfare, quantity is a quality in and of itself.