Potatoes grow off of the stems.  When planting dig a small trench and cover with soil. As the plant grows continue to mount soil over the growth up to about 10-12 inches. The “hills” you have created will support greater yield with your potatoes. Below is a link with additional information. 
https://extension.umn.edu/vegetables/growing-potatoes

I apologize as I misunderstood you were asking about the small size of the potatoes and did not answer the portion of them being green. Green potatoes typically mean they are close to the surface and receiving chlorophyll from the sun. If your potatoes are generally small, even though you hill them, it can be because of the potato variety or nutrients. Each potato variety has “days to maturity”. The longer the days the longer they must stay underground. Potato plants signal the potatoes are ready to harvest when the greenery turns brown and dry. Our growing season does not always support the length of time needed to reach mature size. Another component that impacts size is the nutrients in the soil. Potatoes are heavy feeders and require high nutrients. Below is taken for the link I sent you and explains how to increase nutrients. If you have been following this and still experiencing less yield and green I would suggest having the soil tested. 

Addition of manure or compost can add micronutrients and organic matter to soil.

• Side-dress (place fertilizer alongside of the row) about four weeks after planting.
  • As you hill up soil around the plants, incorporate 0.15 pounds actual nitrogen per 50 feet of row.
  • Repeat the hilling and fertilization two weeks later.