See IGI batch number C01125-2
Frances dtr of Wm and Frances baptised 20th March 1683. (may have died)
A further child Frances, baptised to William & Frances of Brighton 4 May 1690.
Siblings appear under same batch number Susanna 1681, Frances 1683, Nicholas 1685, William 1688, Frances 1690, Elizabeth 1692, Ann 1694, Sarah 1695, William 1697, Hannah 1701.
A note on the IGI for the last William reads: Tne 2nd by this name, 3rd son & 9th child.
that suggests they had at least 3 sons and 6 daughters (not all of whom may have survived)
The SFHG list William senior as having died in 1698, adding that William (1698?), son of Wm & Frances, also died in 1700 and was buried at Rottingdean.
Frances who married Thomas Nevill also in 1711, seems to have had both her brothers called William die in infancy, so should not have been a sibling of the other William Beard who also married in 1711.
Perhaps as a starting point it may therefore help to find a marriage date for William & Frances, the parents of this large Beard family in Brighton around 1680 or even earlier.
Roy G