Если выражение с предлогом at, то в конце непременно будет of! Предлог at указывает на начальный или конечный момент чего-либо —  недели, года, месяца, книги, фильма, урока и т.д,
at the beginning of – в начале месяца, года, фильма и т.д.
at the beginning of the week, at the beginning of the month, at the beginning of the book   
at the end of — в конце недели, урока, книги и т.д.
at the end of June, at the end of the film, at the end of the course

In the beginning — в начале, сначала
in the end — в конце, в конце концов, в конечном счете

после этих выражений нет указаний что именно началось или закончилось
In the beginning, I liked this story. Сначала мне понравилась эта история.
I worked very hard and in the end I managed to get balance while skiing. Я очень усердно трудился и в конце концов мне удалось сохранять равновесие во время катания.
In the end we got home at midnight. В конце концов мы добрались до дома в полночь.

Упражнение на at the beginning/at the end и in the beginning/in the end.

Упражнение.  Complete the sentences with the appropriate prepositions at or in.

1. Mark paused ______ the end of a second passage
2. Notes how to use the dictionary can be found _____ the beginning of the book
3. _____ the end, it all came to nothing.
4. _____ the beginning, I enjoyed the course but I’m getting disappointed now.
5. Police officers will graduate ______ the end of July 2024.
6. We were thinking about going to Italy, but _______the end we went to Austria.
7. I’m busy now, we can talk________ the end of the day.
8. The Bank is planning to make an additional share issue ____ the beginning of next year.
9. ______ the very beginning I realized how difficult the task was.
10. All my life I have had a desire to play pranks, so ____ the end I could not control myself.
11. John remembered it was somewhere ______ the end of Glen Cove Road.

Ответы: 1 At, 2 at, 3 in, 4 in, 5 at, 6 in, 7 at, 8 at, 9 in, 10 in, 11 at