Gap between H4 I94 expiry and H1 I94 start

Few years back I had my H4 extension and first H1 filing at same time. The H4 visa I94 had expiry of 15 days before October 1. I got the H1 approval first with I94 same as of H4 with effective date of October 1st. I had to withdraw my H4 extension to avoid H4 approval coming after H1. I couldn’t leave US before H4 I94 expiry as I had to take a technology training for specific a project that had to start on October 1st and no visa stamping dates were available before that date.

So there was a 15 days gap between H4 I94 expiry and H1 I94 start(both I94 numbers were same). Now I am filling my 485. So to support lawful presence, do I need to submit any additional document for 15 days gap? and what document I can provide for it?

You need to submit copy of all the approved I-797. If USCIS sends you RFE you can explain about the EOS application and why you had to withdraw. I dont think there will be any issue as such as I am guessing your COS from H4 to H1B and the subsequent H1B EOS went fine without any issues.

Got it. The employer had provided I-797 for I-129. So when it comes to submitting all approved I-797, I can submit the I-797 for H4 extension approved in 2014(valid till mid-September 2017) and I-797 of H1 approval(Valid from October 1st 2017 till Mid Sept 2020). Is there a separate I797 for COS from H4 to H1B? and do I need to submit copy of that too?

You won’t have the approval notice as you had withdrawn your COS application.