Beseech is to beg or request in an urgent and anxious manner: “Falling to his knees, the rapist cried, ‘Please, judge, I beseech you to let me go.’ ”
Besiege , on the other hand, means ‘to worry, harass, distress, or to present a request’: “The city residents sought to besiege the mayor to repair the roads before winter.”
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Mnemonics
Beseech= Be+ Seek(Ask money, needy)
Besiege = Be+sieze