extracting special grid cells inside polygones

Hi everyone

I have a shapefile of geology map with 8 fields and 293 polygones. I read this shapefile with shaperead function and display it with mapshow. My case study is a basin with 1764 square kilometer and includes all this 293 geounits polygons. I made my coordinates vectors by [lat,lon]=meshgrat(28.138580:0.009:28.678580,57.075896:0.010242:57.792836) or [X,Y]=meshgrid(57.075896:0.010242:57.786961,28.138580:0.009:28.674729). I dont know how should i overlay this grids and shapefile?

my case study grid is a 61 by 71 matrix between 28.138580 and 28.678580 latitude and 57.075896 and 57.792836 longitude. i wanna assess my work in 1 Kilometer resolution and therefore my grid is an 61 by 71 matrix. My main goal is determine which polygon does any of these cells(not points) located into? My whole cells are 4200 (60*70). I need help and any guides and helps will highly be appreciated.