Dear [Recipient's Name],

I am writing to express my sincere apologies for [specific incident or mistake]. I deeply regret any inconvenience or harm this may have caused you. Please know that it was not my intention to [cause harm or inconvenience], and I am truly sorry for my actions. I value our relationship and hope that you can find it in your heart to forgive me. Thank you for your understanding.

Sincerely,

[Your Name]