In My Opinion. the only given way that you could properly keep a nerite snail along with a betta in such a small tank. is very slim uless you bump up your water change schedule drastically as they have a high bio load and when feeding them, a small amount of food is likely to go un noticed and decay causing a higher rise in ammonia, a better alternative would be more so along the lines or red cherry shrimp, amano shrimp, and ghost shrimp. You should Ideally go along the process of purchasing a siphon first as the debris build up constantly getting stirred up can cause problems. as both nerites and shrimps would find this an unsuitable habitat. you also are aware that the stirring up of debris can leave a negative effect towards your fish at the time, right?