The incidents took place early Friday.
In Jhenaidah, a Bangladeshi was killed as BSF opened fire at him on Baghadanga frontier under Moheshpur upazila. The deceased is Joshim Mondol of Chuadanga.
Border Guard Bangladesh (BGB) 58 Battalion Director Lt Col Tajul Islam said: “A patrolling team of BSF’s Hajrakhal camp saw Jashim when he intruded into Indian territory around 3am Friday.
“They asked him to stop. Later, the BSF personnel opened fire at Jashim when he tried to flee the scene.”
Jashim was declared dead when taken to a hospital in India. "The body will be returned through a flag meeting after autopsy," he added.
Meanwhile in Kurigram, a cattle trader was shot dead by BSF personnel along Gaoitapara border under Roumari upazila.
The deceased is Ful Mia alias Dukhu Mia, son of late Abdul Hye.
Roumari police station OC ABM Sazedul Islam confirmed the matter.