What is they value of a 1935 sterling silver us quarter?

First off, they are not sterling silver, sterling silver is 92.5% pure silver, most silver US Coins are 90% silver and 10% copper, known occasionally as "coin silver". In average circulated condition, the coin is only worth its silver content, at the time of writing, it is about $5.50 in silver content. If it is in mint-state or otherwise very good condition, it might be worth more than just its silver content if you can find a collector.