The correct spelling of the phrase "study at loyalty" is actually "study and loyalty". The /nd/ sound in "and" can sometimes be difficult to hear and it may be pronounced as /n/ or /m/. This can lead to spelling mistakes if one writes "at" instead of "and". Additionally, the word "loyalty" is spelled with a /l/ sound, not a /r/ sound as it may be pronounced in certain dialects. Therefore, it is important to pay attention to both pronunciation and spelling when using this phrase.