No, the 7th note is counting from B, not E. So B, C#, D#, E, F#, G#, A*.
A plain old B chord requires 3 notes: B-D#-F#
If you extend that chord (in the key of E) you must add the next avaiable alternate note to that: A. That note makes the B chord a B7.
If you were in the key of B, and you extend the chord in that key (which is the I chord), then you'd have to add a Bb note (the 7th note of the B scale) and you wind up with a BMaj7.
Now I've really confused you! That's how it works though, and that's where dominant 7th chords come from.
*These 'scales within scales', starting to count from notes OTHER than the 1 are 'the modes'. The V chord's mode is the Mixolydian. It's just like a major scale, only the 7 is flat.
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