Noted from the IGI of entries of Frodsham

Ryc. Pickerne chr. 15 Jan 1595 Frodsham, Cheshire, England
     Father:  Tho.

Tho. Pickeren chr. 28 Jun 1598 Frodsham, Cheshire, England
     Father:  Tho.

Barnbie Pickren chr. 08 Jul 1600 Frodsham, Cheshire, England
     Father:  Thome

Peter Pickeren chr. 04 Jun 1609 Frodsham, Cheshire, England
                        Death 22 Apr 1614
     Father:  Tho.

Perhaps the above Thomas is the same as in this marriage entry:

Tho Pickren married Elnor Ithell  27 Aug 1587  Frodsham, Cheshire, England

Notes: there were many earlier baptisms of Pickering but unfortunately those entries didn’t include the parent’s name at all.

Source:

1.     Baptisms of Frodsham, Cheshire, England.  Familysearch International Genealogical Index  v5.0.  Batch No. P009731, Source Film 0823624 IT 4.  April 22, 2008 Tuesday.

2.     Marriages of Frodsham, Cheshire, England.  Familysearch International Genealogical Index  v5.0.  Batch No. M009731, Source Film 0823624 IT 4.  April 22, 2008 Tuesday.