i believe iOS 9.3 introduced slightly different lookup logic around the apple-app-site-association file and the app handoff feature.

"Handoff first searches for the file in the .well-known subdirectory (for example, https://example.com/.well-known/apple-app-site-association), falling back to the top-level domain if you don’t use the .well-known subdirectory."

see: https://developer.apple.com/library/ios/documentation/UserExperience/Conceptual/Handoff/AdoptingHandoff/AdoptingHandoff.html#//apple_ref/doc/uid/TP40014338-CH2-SW10

I also received the following in my log:

[Mon Feb 29 12:34:53 2016] [error] [source 66.249.75.XXX] File does not exist: /public_path/apple-app-site-association

Where XXX in the log is a number between 0 to 255.

Then, I checked Whois IP 66.249.69.0, 1, 2 ....... 255

And what I found, All IP in range from 66.249.64.0 - 66.249.95.255 assigned to Google Inc. Wait are you kidding me, why google requesting apple-app-site-association on my server?

Because Google extending it's mapping to include information on associations between websites and specific iOS apps for Google App Indexing for universal links from Google Search in Safari..

Whois log for IP 66.249.64.0

NetRange:       66.249.64.0 - 66.249.95.255CIDR:           66.249.64.0/19NetName:        GOOGLENetHandle:      NET-66-249-64-0-1Parent:         NET66 (NET-66-0-0-0-0)NetType:        Direct AllocationOriginAS:       Organization:   Google Inc. (GOGL)RegDate:        2004-03-05Updated:        2012-02-24Ref:            https://whois.arin.net/rest/net/NET-66-249-64-0-1OrgName:        Google Inc.OrgId:          GOGLAddress:        1600 Amphitheatre ParkwayCity:           Mountain ViewStateProv:      CAPostalCode:     94043Country:        USRegDate:        2000-03-30Updated:        2015-11-06Ref:            https://whois.arin.net/rest/org/GOGLOrgAbuseHandle: ABUSE5250-ARINOrgAbuseName:   AbuseOrgAbusePhone:  +1-650-253-0000 OrgAbuseEmail:  email@google.comOrgAbuseRef:    https://whois.arin.net/rest/poc/ABUSE5250-ARINOrgTechHandle: ZG39-ARINOrgTechName:   Google IncOrgTechPhone:  +1-650-253-0000 OrgTechEmail:  email@google.comOrgTechRef:    https://whois.arin.net/rest/poc/ZG39-ARIN

Since iOS 9.3 Apple will first try to download /.well-known/apple-app-site-association and in case it fails it fallbacks to /apple-app-site-association.

See Apple's Technical Q&A QA1919:

Incoming requests for /.well-known/apple-app-site-association file

Q: Why is my web server receiving requests for https://example.com/.well-known/apple-app-site-association?

A: The recently released iOS 9.3 update implements RFC 5785. Because of this, devices running iOS 9.3 will first request /.well-known/apple-app-site-association for the apple-app-site-association file that is required to implement Universal Links and Shared Web Credentials. If the file is not found in this location, then the device will request the file in the root of the web server, as with prior releases of iOS 9.