Yes, you can cook frozen food in a small fryer. Small fryers, including air fryers and deep fryers, are versatile kitchen appliances that can handle a variety of frozen foods such as fries, chicken nuggets, fish sticks, and more. 
When using an air fryer, preheat it to the recommended temperature, usually between 350°F to 400°F (175°C to 200°C), depending on the food. Arrange the frozen food in a single layer in the fryer basket to ensure even cooking. Shake the basket halfway through the cooking time to promote uniform crispiness. Air fryers use hot air circulation to cook food, resulting in a crispy texture similar to deep frying but with less oil.
For deep fryers, preheat the oil to the appropriate temperature, typically around 350°F (175°C). Carefully lower the frozen food into the hot oil using a fryer basket or tongs to avoid splattering. Cook until the food is golden brown and reaches the desired level of crispiness. Deep frying frozen food can yield a crunchy exterior and moist interior, but it requires more oil than air frying.
Regardless of the method, always check the internal temperature of the food to ensure it is cooked thoroughly. Use a food thermometer to verify that it has reached a safe temperature, usually 165°F (74°C) for most frozen foods. Follow the cooking instructions on the packaging for best results, and adjust cooking times based on the specific fryer model and food type.