Intrusion is a feature of connected speech. When two words are said together, an extra sound is sometimes placed between them in order to make them easier to say.
When a native speaker says 'I am not happy' there is an intrusive /j/ sound between 'I' and 'am' which makes it easier to say the phrase quickly.
In the classroom
Teachers can help learners hear and recognise the words and sounds involved through asking students to predict where in a dialogue they might hear intrusive sounds, and then listening to check.