我的电脑旁边没放着饮料。this sentence is correct. but we usually say it like this 我的电脑旁边没有放<s style="background-color: rgb(255, 153, 0);">着</s>饮料(there isn't any soft drink near my computer) or 我的电脑旁边没<s style="background-color: rgb(255, 153, 0);">放着</s>有饮料
on the contrary meaning 我的电脑旁边<s style="background-color: rgb(255, 153, 0);">没</s>放着饮料 (there is a bottle of soft drink next to my computer)